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Dissertations / Theses on the topic 'Representation of the symmetric group'

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Published: 4 June 2021

Last updated: 14 February 2022

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1

George, Timothy Edward. "Symmetric representation of elements of finite groups." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.

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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.

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2

Kangwai, Riki Dale. "The analysis of symmetric structures using group representation theory." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/265422.

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Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.

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3

Norton, Elizabeth. "Representations and the Symmetric Group." Scholarship @ Claremont, 2002. https://scholarship.claremont.edu/hmc_theses/139.

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The regular representation of the symmetric group Sn is a vector space of dimension n! with many interesting invariant subspaces. The projections of a vector onto these subspaces may be computed by first considering projections onto certain basis elements in the subspace and then recombining later. If all of these projections are kept, it creates an explosion in the size of the data, making it difficult to store and work with. This is a study of techniques to compress this computed data such that it is of the same dimmension as the original vector.

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4

Kreighbaum, Kevin M. "Combinatorial Problems Related to the Representation Theory of the Symmetric Group." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1270830566.

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5

Banister, Melissa. "Separating Sets for the Alternating and Dihedral Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/158.

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This thesis presents the results of an investigation into the representation theory of the alternating and dihedral groups and explores how their irreducible representations can be distinguished with the use of class sums.

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6

Russell, Lee. "Modular representations of the symmetric group." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627178.

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7

Scopes, Joanna. "Representations of the symmetric groups." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279989.

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8

Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5, A52, 2• A52, 2 : A62, PSL(2,49), 28 : A5, PGL(2,19), PSL(2,71), 24 : A5, 24 : A6, PSL(2,7), 3 x PSL(3,4), 2• PSL(3,4), PSL(3,4), 2• (M12 : 2), 37:S7, 35 : S5, S6, 25 : S6, 35 : S6, 25 : S5, 24 : S6, and M12 as homomorphic images of the permutation progenitors 2*60 : (2 x A5), 2*60 : A5, 2*21 : (7: 3), 2*60 : (2 x A5), 2*120 : S5, and 2*144 : (32 : 24). We have given original proof of the 2*n Symmetric Presentation Theorem. In addition, we have also provided original proof for the Extension of the Factoring Lemma (involutory and non-involutory progenitors). We have constructed S5, PSL(2,7), and U(3,5):2 using the technique of double coset enumeration and by way of linear fractional mappings. Furthermore, we have given proofs of isomorphism types for 7 x 22, U(3,5):2, 2•(M12 : 2), and (4 x 2) :• 22.

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9

Harris, Elena Yavorska. "Symmetric representation of elements of sporadic groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2844.

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Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.

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10

Vercheval, Nicolas. "The Representation of Symmetric Groups in Two-Dimensional Persistent Homology." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13545/.

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The two dimensional persistent homology, that can be reduced to the homology of a family of parameterized real functions, can be found to have some issues due to a phenomenon of monodromy, which happens when a loop in the parameters' space doesn't translate into loops of the elements of the persistent diagram. Instead they switch place between them in a functorial way. In this paper we present a formalisation of this functor and we will make an use of it, representing an arbitrary symmetric group by means of a suitable filtering function.

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11

Moreira, Rodriguez Rivera Walter. "Products of representations of the symmetric group and non-commutative versions." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85938.

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We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate the internal and external products to the composition and convolution of linear endomorphisms of the tensor algebra. The new product we construct corresponds to the Heisenberg product of endomorphisms of the tensor algebra. For symmetric functions, the Heisenberg product is given by a construction which combines induction and restriction of representations. For non-commutative symmetric functions, the structure constants of the Heisenberg product are given by an explicit combinatorial rule which extends a well-known result of Garsia, Remmel, Reutenauer, and Solomon for the descent algebra. We describe the dual operation among quasi-symmetric functions in terms of alphabets.

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12

Yaseen, Abdul Kareem Abdul Rahman. "Modular spin representations of the symmetric group." Thesis, Aberystwyth University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491551.

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13

Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

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This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

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14

Cioppa, Timothy. "The Modern Representation Theory of the Symmetric Groups." Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20490.

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The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

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15

Paget, Rowena. "Representation theory of symmetric groups and related algebras." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270235.

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16

Newhouse, Jack. "Explorations of the Aldous Order on Representations of the Symmetric Group." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/35.

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The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements.

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17

Rai, Suranjana, Jagdish Rai, and Andreas Cap@esi ac at. "Group--Theoretical Structure of the Entangled States of N Identical." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi904.ps.

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18

Franjou, Vincent. "Modules et algebres instables sur l'algebre de steenrod : une etude aux nilpotents pres." Nantes, 1988. http://www.theses.fr/1988NANT2003.

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L'algebre de cohomologie modulo 2 d'un espace est un module instable sur l'algebre de steenrod a. Le premier chapitre etudie la categorie abelienne obtenue comme quotient de la categorie des a-modules instables par sa sous-categorie des a-modules nilpotents. On definit d'abord une notion de poids qui induit une filtration naturelle sur tout a-module instable. Cela nous permet de classifier les objets simples par les representations modulaires simples des groupes symetriques. La cohomologie des classifiants des 2-groupes abeliens elementaires est etudiee en exemple. On obtient aussi que notre categorie est localement finie, et on classifie ses objets injectifs. Le second chapitre se propose de representer les a-algebres instables par des diagrammes, similaires a ceux que quillen introduit pour la cohomologie des groupes compacts. Plus precisement, on associe a toute a-algebre instable une categorie qui permet de la reconstruire "aux nilpotents pres". On en obtient une simplification illustree par des exemples

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19

Lyle, Sinead. "Some topics in the representation theory of the symmetric and general linear groups." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401808.

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20

Trinh, Megan. "On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246.

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21

Nash, David A. 1982. "Graded representation theory of Hecke algebras." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10871.

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xii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm to compute several examples and to obtain a closed form for the graded decomposition numbers in the case of two-column partitions. In this case, we also precisely describe the 'reduction modulo p' process, which relates the graded irreducible representations of Hd over [Special characters omitted.] at a p th -root of unity to those of the group algebra of the symmetric group over a field of characteristic p.<br>Committee in charge: Alexander Kleshchev, Chairperson, Mathematics; Jonathan Brundan, Member, Mathematics; Boris Botvinnik, Member, Mathematics; Victor Ostrik, Member, Mathematics; William Harbaugh, Outside Member, Economics

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22

Whitehouse, Sarah Ann. "Gamma (co)homology of commutative algebras and some related representations of the symmetric group." Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/4214/.

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This thesis covers two related subjects: homology of commutative algebras and certain representations of the symmetric group. There are several different formulations of commutative algebra homology, all of which are known to agree when one works over a field of characteristic zero. During 1991-1992 my supervisor, Dr. Alan Robinson, motivated by homotopy-theoretic ideas, developed a new theory, Γ-homology [Rob, 2]. This is a homology theory for commutative rings, and more generally rings commutative up to homotopy. We consider the algebraic version of the theory. Chapter I covers background material and Chapter II describes Γ-homology. We arrive at a spectral sequence for Γ-homology, involving objects called tree spaces. Chapter III is devoted to consideration of the case where we work over a field of characteristic zero. In this case the spectral sequence collapses. The tree space, Tn, which is used to describe Γ-homology has a natural action of the symmetric group Sn. We identify the representation of Sn on its only non-trivial homology group as that given by the first Eulerian idempotent en(l) in QSn. Using this, we prove that Γ-homology coincides with the existing theories over a field of characteristic zero. In fact, the tree space, Tn, gives a representation of Sn+l. In Chapter IV we calculate the character of this representation. Moreover, we show that each Eulerian representation of Sn is the restriction of a representation of Sn+1. These Eulerian representations are given by idempotents en(j), for j=1, ..., n, in QSn, and occur in the work of Barr [B], Gerstenhaber and Schack [G-S, 1], Loday [L, 1,2,3] and Hanlon [H]. They have been used to give decompositions of the Hochschild and cyclic homology of commutative algebras in characteristic zero. We describe our representations of Sn+1 as virtual representations, and give some partial results on their decompositions into irreducible components. In Chapter V we return to commutative algebra homology, now considered in prime characteristic. We give a corrected version of Gerstenhaber and Schack's [G-S, 2] decomposition of Hochschild homology in this setting, and give the analagous decomposition of cyclic homology. Finally, we give a counterexample to a conjecture of Barr, which states that a certain modification of Harrison cohomology should coincide with André/Quillen cohomology.

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23

Pezzoli, Gian Marco. "Representations of symmetric groups on the homology of dual matroids of complete graphs." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18253/.

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This thesis investigates the representations of the symmetric group on the homology of the dual matroid of a complete graph. These representations arise as follows: with each graph we can associate a matroid, by taking the set of edges of the graph as ground set and the edge sets of simple cycles as the circuits of the matroid. We focus on the dual of the matroid of the complete graph. We calculate the homology of the simplicial complex L associated with this matroid. Permuting the vertices of the complete graph induces a permutation on the edge set which is a vertex map of the simplicial complex. This vertex map sends independents to independents, thus inducing a simplicial map from the polytope of L to itself, hence on the homology spaces of L. This defines a representation of the symmetric group on the homology Hi(L,C). We show that the above representation is induced from a primitive representation of the cyclic subgroup of order n.

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24

Frączyk, Mikołaj. "Benjamini-Schramm convergence of locally symmetric spaces." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS233/document.

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Le sujet principal de ce mémoire est le comportement asymptotique de la géométrie et topologie des variétés localement symétriques Gamma\ X quand le volume tend vers l’infini. Notre premier résultat porte sur la convergence Benjamini-Schramm des 2 ou 3-variétés hyperboliques arithmétiques. Une suite d'espaces localement symétriques (Gamma_n\ X) converge Benjamini-Schramm vers l'espace symétrique X si pour chaque R>0 la limite de \Vol((\Gamma\X)_{<br>The main theme of this work is the study of geometry and topology of locally symmetric spaces Gamma\ X as ther volume Vol(\Gamma\ X) tends to infinity. Our first main result concerns the Benjamini-Schramm convergence for arithmetic hyperbolic 2 or 3-manifolds. A sequence of locally symmetric spaces (Gamma_n\ X) converges Benjamini-Schramm to X if and only if for every radius R>0 the limit Vol((Gamma\ X)_{

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25

Bogdanic, Dusko. "Graded blocks of group algebras." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:faeaaeab-1fe6-46a9-8cbb-f3f633131a73.

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In this thesis we study gradings on blocks of group algebras. The motivation to study gradings on blocks of group algebras and their transfer via derived and stable equivalences originates from some of the most important open conjectures in representation theory, such as Broue’s abelian defect group conjecture. This conjecture predicts the existence of derived equivalences between categories of modules. Some attempts to prove Broue’s conjecture by lifting stable equivalences to derived equivalences highlight the importance of understanding the connection between transferring gradings via stable equivalences and transferring gradings via derived equivalences. The main idea that we use is the following. We start with an algebra which can be easily graded, and transfer this grading via derived or stable equivalence to another algebra which is not easily graded. We investigate the properties of the resulting grading. In the first chapter we list the background results that will be used in this thesis. In the second chapter we study gradings on Brauer tree algebras, a class of algebras that contains blocks of group algebras with cyclic defect groups. We show that there is a unique grading up to graded Morita equivalence and rescaling on an arbitrary basic Brauer tree algebra. The third chapter is devoted to the study of gradings on tame blocks of group algebras. We study extensively the class of blocks with dihedral defect groups. We investigate the existence, positivity and tightness of gradings, and we classify all gradings on these blocks up to graded Morita equivalence. The last chapter deals with the problem of transferring gradings via stable equivalences between blocks of group algebras. We demonstrate on three examples how such a transfer via stable equivalences is achieved between Brauer correspondents, where the group in question is a TI group.

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26

Montagard, Pierre-Louis. "Une nouvelle propriété de stabilité du pléthysme et quelques conséquences." Université Joseph Fourier (Grenoble), 1995. http://www.theses.fr/1995GRE10164.

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Depuis les travaux de schur et weyl, on sait que les representations irreductibles et polynomiales du groupe lineaire d'un espace vectoriel complexe de dimension finie v sont parametrees par les partitions, c'est a dire par les suites finies decroissantes d'entiers positifs. De plus, ces representations peuvent etre calculees en appliquant a v un foncteur (le foncteur de schur). Ce qui permet de definir le plethysme comme la composition de deux foncteurs de schur, par exemple la composition de deux puissances symetriques. Dans ce travail, nous etudions l'evolution des multiplicites de certaines composantes lorsqu'on fait croitre les parts de la partition qui definit le plethysme. Nous obtenons une propriete tres generale de croissance et de stabilite, dans le cas ou on applique un foncteur de schur a une representation irreductible d'un groupe algebrique reductif. Nous appliquons ensuite cette propriete au groupe lineaire de v. Ce qui nous permet d'obtenir des conditions necessaires pour qu'une representation irreductible apparaisse dans un plethysme. Ces conditions sont sous la forme d'inequations lineaires dans les parts des partitions definissant la representation irreductible et le foncteur de schur. Nous obtenons un resultat analogue pour la decomposition du produit tensoriel de deux representations quelconques du groupe symetrique

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27

Knight, Jason. "Various methods for calculating reducible and irreducible representations of the symmetric group a thesis presented to the faculty of the Graduate School, Tennessee Technological University /." Click to access online, 2009. http://proquest.umi.com/pqdweb?index=30&sid=1&srchmode=1&vinst=PROD&fmt=6&startpage=-1&clientid=28564&vname=PQD&RQT=309&did=1760001861&scaling=FULL&ts=1251310430&vtype=PQD&rqt=309&TS=1251310467&clientId=28564.

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28

Nazzal, Lamies Joureus. "Homomorphic images of semi-direct products." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2770.

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The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.

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29

Wasserman, Benjamin. "Variétés magnifiques de rang deux." Grenoble 1, 1997. http://www.theses.fr/1997GRE10037.

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Soit g un groupe reductif complexe (connexe). Les g-varietes magnifiques les plus connues sont celles de rang zero, a savoir les varietes de drapeaux generalisees g/p, celles de rang un, classifiees par akhiezer, et certaines varietes symetriques completes decrites par de concini et procesi comme par exemple le celebre espace des coniques completes. Il y a recemment un interet renouvele pour les varietes magnifiques de rang deux car des travaux de luna, brion, pauer et knop montrent que celles-ci jouent un role clef dans la theorie des varietes spheriques. L'objectif de ce travail est la classification des varietes magnifiques de rang deux. Ces dernieres peuvent se caracteriser de la maniere suivante. Ce sont des g-varietes lisses completes contenant quatre orbites, a savoir une orbite dense et deux orbites de codimension un dont les adherences d#1 et d#2 se coupent transversalement en la quatrieme orbite qui est de codimension deux. Nous avons recueilli nos resultats dans des tables, contenant groupes d'isotropie et donnees combinatoires en rapport avec la theorie des varietes spheriques.

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30

Hannesson, Sigurdur. "Representations of symmetric groups." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442464.

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31

Wildon, Mark. "Modular representations of symmetric groups." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403775.

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32

Fayers, Matthew. "Representations of symmetric groups and Schur algebras." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620642.

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33

Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.

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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

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Phillips, Aaron M. "Restricting modular spin representations of symmetric and alternating groups /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3095271.

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Thesis (Ph. D.)--University of Oregon, 2003.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 69-71). Also available for download via the World Wide Web; free to University of Oregon users.

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35

Hall, Jack Kingsbury Mathematics &amp Statistics Faculty of Science UNSW. "Some branching rules for GL(N,C)." Awarded by:University of New South Wales. Mathematics and Statistics, 2007. http://handle.unsw.edu.au/1959.4/29473.

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This thesis considers symmetric functions and algebraic combinatorics via the polynomial representation theory of GL(N,C). In particular, we utilise the theory of Jacobi-Trudi determinants to prove some new results pertaining to the Littlewood-Richardson coefficients. Our results imply, under some hypotheses on the strictness of the partition an equality between Littlewood-Richardson coefficients and Kostka numbers. For the case that a suitable partition has two rows, an explicit formula is then obtained for the Littlewood-Richardson coefficient using the Hook Length formula. All these results are then applied to compute branching laws for GL(m+n,C) restricting to GL(m,C) x GL(n,C). The technique also implies the well-known Racah formula.

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Ferreira, Sarah Ribeiro de Jesus. "Combinatória das representações irredutíveis do grupo simétrico." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7573.

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Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-09-20T13:36:29Z No. of bitstreams: 1 sarahribeirodejesusferreira.pdf: 854513 bytes, checksum: bdb519074051d0889c62002f16fe1a8e (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-10-01T19:17:08Z (GMT) No. of bitstreams: 1 sarahribeirodejesusferreira.pdf: 854513 bytes, checksum: bdb519074051d0889c62002f16fe1a8e (MD5)<br>Made available in DSpace on 2018-10-01T19:17:08Z (GMT). No. of bitstreams: 1 sarahribeirodejesusferreira.pdf: 854513 bytes, checksum: bdb519074051d0889c62002f16fe1a8e (MD5) Previous issue date: 2018-08-13<br>Nesse trabalho, apresentamos a teoria de representação básica do grupo simétrico e seus aspectos combinatórios. O objetivo principal desse trabalho é construir um conjunto completo de representações irredutíveis e não equivalentes do grupo simétrico, em termos da sua partição e conceitos combinatórios relacionados com o tableau de Young. Veremos que esse objeto combinatório nos fornecerá duas maneiras de descrever as representações irredutíveis do grupo simétrico, uma via politablóides e uma alternativa via idempotentes da álgebra de grupo, e que, na verdade, essas duas abordagens são isomorfas. Iremos abordar alguns resultados interessantes, como a regra de Young, a regra da ramificação e o algoritmo combinatório da correspondência de Robinson-Schensted.<br>In this work, we present the basic representation theory of the symmetric group and its combinatorial aspects. The main objective of this work is to construct a complete set of irreducible and inequivalent representations of the symmetric group, in terms of its partition and combinatorial concepts related to Young’s tableau. We will see that this combinatorial object will provide us two ways of describing the irreducible representations of the symmetric group, a politabloid pathway, and an alternative via idempotent group algebra, and that, in fact, these two approaches are isomorphic. We will cover some interesting results, such as the Young’s rule, the branching rule, and the Robinson-Schensted’s combinatorial matching algorithm.

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37

Farber, Lee. "Symmetric generation of finite homomorphic images?" CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2901.

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The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.

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38

Ruff, Oliver. "Completely splittable representations of symmetric groups and affine Hecke algebras /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190545.

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Thesis (Ph. D.)--University of Oregon, 2005.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

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39

Hill, David Edward. "The Jantzen-Shapovalov form and Cartan invariants of symmetric groups and Hecke algebras /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959351&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2007.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 107-108). Also available for download via the World Wide Web; free to University of Oregon users.

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40

Williams, Adrian Leonard. "Some more decomposition numbers for modular representations of symmetric groups." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313541.

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41

Salam, M. A. "Symmetric functions and the symmetric group Sn." Thesis, University of Canterbury. Physics, 1991. http://hdl.handle.net/10092/8161.

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A simple method for the embedding On → Sn of ordinary and spin irreps in both n-dependent notation and an n-independent reduced notation is given. Basic spin irreps and ordinary irreps are combined using the properties of Q-functions and raising operators in order to give a complete set of branching rules of On → Sn for spin irreps. The modification rules for Q-functions given by Morris are redefined to yield a complete and unambiguous set of rules. Properties of shifted tableaux have been explored in order to improve the algorithm for the calculation of Q-function outer products. A simple technique has been established for finding out the highest and lowest partitions in the expansion of Q-function outer products. Using these techniques and Young's raising operators, the Kronecker product for Sn spin irreps has been completed. A number of properties of Young's raising operator as applied to S-functions and Schur's Q-functions are noted. The order of evaluating the action of inverse raising operators is found to require careful specification and the maximum power of the operators δij is determined. The operation of inverse raising operator on a partition λ is found to be the same as for its conjugate λ. A new definition of Shifted Lattice Property that can efficiently remove all the dead tableaux in the Q-function analogue of the Littlewood-Richardson rule is introduced. A simple combinatorial analogue of raising and inverse raising operators is given. The q-deformation of symmetric functions is introduced leading to q-analogues of many well-known relationships in the theory of symmetric functions. A q-analogue of the spin and ordinary characters of Sn is given by making use of a method that closely parallels that of quantum groups. This formalism leads to a very simple technique for the construction of twisted and untwisted q-vertex operators. An isomorphism between the space of q-vertex operators and the ring of q-deformed Hall-Littlewood symmetric functions has been found.

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42

Wickramasekara, Sujeewa, and sujeewa@physics utexas edu. "Symmetry Representations in the Rigged Hilbert Space Formulation of." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi993.ps.

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43

Germano, Guilherme Rocha. "Representações irredutíveis unitárias do grupo de Poincaré." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-08122016-160042/.

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A teoria de representações de grupos topológicos Hausdorff, localmente compactos e separáveis em espaços de Hilbert separáveis é introduzida, especificada para grupos compactos e comutativos e são obtidas realizações explicitas das representações finitas irredutíveis de $SU(2)$, $SO(3)$, SL(2,C) e $SO(1,3)^{\\uparrow}$. A teoria das representações induzidas é então apresentada e, depois de feita a conexão entre teorias quântico relativísticas livres no espaço plano de Minkowski e representações unitárias irredutíveis de $R^4 times$ SL(2,C), aplicada para obter tais representações e realizar explicitamente os casos correspondentes a partículas elementares com spin definido em espaços que não admitem a definição de operadores de reflexão espacial. A inclusão da operação de reflexão espacial é feita através de uma variação do método das representações induzidas que conduz a representações unitárias {\\bf redutíveis} de $R^4 times$ SL(2,C) para as quais são obtidas equações de onda selecionando espaços irredutíveis, os quais definem partículas elementares admitindo paridade no contexto das teorias quânticas de campos livres.<br>The theory of locally compact, second countable and Hausdorff topological group representations in separable Hilbert spaces is introduced, and specified to compact and commutative groups. Explicit realizations of the finite irreducible representations of $SU(2)$, $SO(3)$, SL(2,C) and $SO(1,3)^{\\uparrow}$ are obtained. The theory of induced representations is then presented and, after the connection between quantum relativistic free theories in flat Minkowski space and unitary irreducible representations of $R^4 times$ SL(2,C) is made, it is applied and used to classify these representations. Explicit realizations of the cases corresponding to elementary particles with definite spin in spaces which do not allow spacial reflection operators are presented. Spacial reflections are carried with a variation of the induced representation method that leads to unitary {\\bf reducible} representations of $R^4 times$ SL(2,C). Wave equations selecting irreducible spaces that define elementary particles admitting parity in quantum free field theories are derived.

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44

Black, Samson 1979. "Representations of Hecke algebras and the Alexander polynomial." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10847.

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viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combinatorial proof of this result.<br>Committee in charge: Arkady Vaintrob, Co-Chairperson, Mathematics Jonathan Brundan, Co-Chairperson, Mathematics; Victor Ostrik, Member, Mathematics; Dev Sinha, Member, Mathematics; Paul van Donkelaar, Outside Member, Human Physiology

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45

Fonseca, Marlon Pimenta. "Representações dos grupos simétrico e alternante e aplicações às identidades polinomiais." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5912.

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Made available in DSpace on 2016-06-02T20:28:31Z (GMT). No. of bitstreams: 1 6450.pdf: 757192 bytes, checksum: 765b66ca6aed0686ecbcd10c145cefac (MD5) Previous issue date: 2014-11-28<br>Financiadora de Estudos e Projetos<br>In this dissertation we ll present a discussion about the Representations of the Symmetric Group Sn and Alternating Group An. We ll study basics results of the Young s Theory about the representations of the Symmetric Group and discover the decomposition of the algebra FSn in simple subalgebras. After, we ll utilize this decomposition to find the decomposition of the algebra FAn in simple subalgebras. Finally, we ll use this decompositions, together with the PI Theory, for get the sequence of A-codimensions for the Grassmann Algebra (Exterior Algebra) infinitely generated.<br>Neste trabalho apresentamos uma discussão a respeito das Representações dos Grupos Simétrico Sn e do Grupo Alternante An. Estudaremos resultados básicos da Teoria de Young sobre as representações do grupo simétrico para encontrarmos a decomposição da álgebra de grupo FSn em subálgebras simples. Depois utilizaremos tal decomposição para encontrar a decomposição da álgebra de grupo FAn em subálgebras simples. Por fim empregaremos as informações a respeito das decomposições acima citadas, juntamente com a PI-Teoria, para obter a sequência de A-codimensões para a álgebra de Grassmann (álgebra exterior) infinitamente gerada.

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46

Nguyen, Benny. "Symmetrically generated groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2902.

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This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.

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Chan, Chou Sin. "Representation of symmetric instability in large scale models." Thesis, University of Reading, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358408.

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48

Tan, Kai Meng. "Small defect blocks of symmetric group algebras." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624153.

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49

Gerber, Thomas. "Matrices de décomposition des algèbres d'Ariki-Koike et isomorphismes de cristaux dans les espaces de Fock." Phd thesis, Université François Rabelais - Tours, 2014. http://tel.archives-ouvertes.fr/tel-01057480.

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Cette thèse est consacrée à l'étude des représentations modulaires des algèbres d'Ariki-Koike, et des liens avec la théorie des cristaux et des bases canoniques de Kashiwara via le théorème de catégorification d'Ariki. Dans un premier temps, on étudie, grâce à des outils combinatoires, les matrices de décomposition de ces algèbres en généralisant les travaux de Geck et Jacon. On classifie entièrement les cas d'existence et de non-existence d'ensembles basiques, en construisant explicitement ces ensembles lorsqu'ils existent. On explicite ensuite les isomorphismes de cristaux pour les représentations de Fock de l'algèbre affine quantique de type A affine. On construit alors un isomorphisme particulier, dit canonique, qui permet entre autres une caractérisation non-récursive de n'importe quelle composante connexe du cristal. On souligne également les liens avec la combinatoire des mots sous-jacente à la structure cristalline des espaces de Fock, en décrivant notamment un analogue de la correspondance de Robinson-Schensted-Knuth pour le type A affine.

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Cook, Joseph. "Properties of eigenvalues on Riemann surfaces with large symmetry groups." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/36294.

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On compact Riemann surfaces, the Laplacian $\Delta$ has a discrete, non-negative spectrum of eigenvalues $\{\lambda_{i}\}$ of finite multiplicity. The spectrum is intrinsically linked to the geometry of the surface. In this work, we consider surfaces of constant negative curvature with a large symmetry group. It is not possible to explicitly calculate the eigenvalues for surfaces in this class, so we combine group theoretic and analytical methods to derive results about the spectrum. In particular, we focus on the Bolza surface and the Klein quartic. These have the highest order symmetry groups among compact Riemann surfaces of genera 2 and 3 respectively. The full automorphism group of the Bolza surface is isomorphic to $\mathrm{GL}_{2}(\mathbb{Z}_{3})\rtimes\mathbb{Z}_{2}. We analyze the irreducible representations of this group and prove that the multiplicity of $\lambda_{1}$ is 3, building on the work of Jenni, and identify the irreducible representation that corresponds to this eigenspace. This proof relies on a certain conjecture, for which we give substantial numerical evidence and a hopeful method for proving. We go on to show that $\lambda_{2}$ has multiplicity 4.

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