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Dissertations / Theses on the topic 'Representations of groups'

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Published: 4 June 2021

Last updated: 28 July 2024

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1

Andrus, Ivan B. "Matrix Representations of Automorphism Groups of Free Groups." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd856.pdf.

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2

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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3

Stavis, Andreas. "Representations of finite groups." Thesis, Karlstads universitet, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69642.

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Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of

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4

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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5

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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6

Lawrence, Ruth Jayne. "Homology representations of braid groups." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236125.

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7

Towers, Matthew John. "Modular representations of p-groups." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427611.

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8

Can, Himmet. "Representations of complex reflection groups." Thesis, Aberystwyth University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289795.

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9

Cai, Yuanqing. "Theta representations on covering groups." Thesis, Boston College, 2017. http://hdl.handle.net/2345/bc-ir:107492.

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Thesis advisor: Solomon Friedberg<br>Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondl

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10

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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11

Iano-Fletcher, Maria. "Polynomial representations of symplectic groups." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/89157/.

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In Chapter 1 we review some of the classical theory of reductive algebraic groups over an algebraically closed field. In Chapter 2 we summarise the work of Green on polynomial representations of GLn(k) where k is an infinite field. The irreducible polynomial representations of degree r of GLn(k) are parametrised by partitions λ of r. The irreducible polynomial GLn(k)-module F λ k can be obtained in two ways, as the quotient of a Weyl module V λ k by its unique maximal submodule, or as the unique minimal submodule of a Shur module D λ k. The two modules V λ k and D λ k are duals of one another.

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12

MANARA, ELIA. "Multiplicative representations of surface groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2018. http://hdl.handle.net/10281/199017.

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Un gruppo di superficie è (isomorfo) al gruppo fondamentale di una superficie orientabile chiusa di genere k (maggiore o uguale a 2). È uno small cancellation group e quindi iperbolico; il suo grafo di Cayley è isomorfo a una tassellatura del piano iperbolico fatta di 2k-goni iperbolici. È possibile definire alcuni sottoinsiemi del grafo di Cayley, detti “coni”, su cui il gruppo agisce con un numero finito di orbite, chiamate “cono tipi”. Una rappresentazione moltiplicativa di un gruppo di superficie è una rappresentazione unitaria definita sullo spazio di Hilbert delle funzioni moltiplicativ

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13

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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14

Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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15

Szechtman, Fernando. "Weil representations of finite symplectic groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0006/NQ39598.pdf.

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16

Quinlan, Rachel. "Irreducible projective representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59658.pdf.

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17

Benjamin, Ian Francis. "Quasi-permutation representations of finite groups." Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250561.

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18

Martin, Benjamin Michael Sinclair. "Varieties of representations of surface groups." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243429.

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19

Nabney, Ian Thomas. "Soluble minimax groups and their representations." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333316.

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20

Mason-Brown, Lucas(Lucas David). "Unipotent representations of real reductive groups." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126931.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020<br>Cataloged from the official PDF of thesis.<br>Includes bibliographical references (pages 207-210).<br>Let G be a real reductive group and let Ĝ be the set of irreducible unitary representations of G. The determination of Ĝ (for arbitrary G) is one of the fundamental unsolved problems in representation theory. In the early 1980s, Arthur introduced a finite set Unip(G) of (conjecturally unitary) irreducible representations of G called unipotent representations. In a certain sense, these representations

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21

Ronquillo, Rivera Javier Alfredo. "Extremely Amenable Groups and Banach Representations." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520548085599864.

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22

Anwar, Muhammad F. "Representations and cohomology of algebraic groups." Thesis, University of York, 2011. http://etheses.whiterose.ac.uk/2032/.

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Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In [11], Donkin gave a recursive description for the characters of cohomology of line bundles on the flag variety G/B with G = SL3. In chapter 2 of this thesis we try to give a non recursive description for these characters. In chapter 3, we give the first step of a version of formulae in [11] for G = G2. In his famous paper [7], Demazure introduced certain indecomposable modules and used them to give a short proof of the Borel-Weil-Bott theorem (characteristic zero). In chap

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23

Chan, Ping-Shun. "Invariant representations of GSp(2)." Columbus, Ohio : Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1132765381.

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24

Sun, Binyong. "Matrix coefficients and representations of real reductive groups /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20SUN.

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25

O'Sullivan, Clodagh M. "Tolerance in intergroup relations: cognitive representations reducing ingroup projection." Thesis, University of Fort Hare, 2008. http://hdl.handle.net/10353/140.

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This study assessed the personal, career and learning skills needs of 196 psychology students (M= 56, F= 103). The preferred means of counselling assistance, preferred experience of counselling and preferred counselling provider were also assessed. The most highly endorsed needs were time management skills (83.5 pecent, n=162), learning test-taking strategies (82 percent, n=159), job search strategies (73.6 percent, n=142), increasing self-confidence (70.3 percent, n=135), increasing motivation (72.4 percent, n=134), controlling anxiety and nervousness (68.7 percent, n=134), public speaking an

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26

Kielak, Dawid. "Free and linear representations of outer automorphism groups of free groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:f2045fba-1546-4dd3-af9f-7d02c4fc505e.

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For various values of n and m we investigate homomorphisms from Out(F_n) to Out(F_m) and from Out(F_n) to GL_m(K), i.e. the free and linear representations of Out(F_n) respectively. By means of a series of arguments revolving around the representation theory of finite symmetric subgroups of Out(F_n) we prove that each homomorphism from Out(F_n) to GL_m(K) factors through the natural map p_n from Out(F_n) to GL(H_1(F_n,Z)) = GL_n(Z) whenever n=3, m < 7 and char(K) is not an element of {2,3}, and whenever n>5, m< n(n+1)/2 and char(K) is not an element of {2,3,...,n+1}. We also construct a new in

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27

Gu, Jerin. "Single-petaled K-types and Weyl group representations for classical groups." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43735.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (p. 135-137).<br>In this thesis, we show that single-petaled K-types and quasi-single-petaled K-types for reductive Lie groups generalize petite K-types for split groups. First, we prove that a Weyl group algebra element represents the action of the long intertwining operator for each single-petaled K-type, and then we demons

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28

Martin, Stuart. "Quivers and the modular representation theory of finite groups." Thesis, University of Oxford, 1988. http://ora.ox.ac.uk/objects/uuid:59d4dc72-60e5-4424-9e3c-650eb2b1d050.

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The purpose of this thesis is to discuss the rôle of certain types of quiver which appear in the modular representation theory of finite groups. It is our concern to study two different types of quiver. First of all we construct the ordinary quiver of certain blocks of defect 2 of the symmetric group, and then apply our results to the alternating group and to the theory of partitions. Secondly, we consider connected components of the stable Auslander-Reiten quiver of certain groups G with normal subgroup N. The main interest lies in comparing the tree class of components of N-modules, with the

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29

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

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30

Hindeleh, Firas. "Tangent and cotangent bundles automorphism groups and representations of Lie groups /." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2006. http://www.ohiolink.edu/etd/view.cgi?acc_num=toledo1153933389.

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Thesis (Ph.D.)--University of Toledo, 2006.<br>Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.

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31

Evseeva, Elena. "Représentations du groupe pseudo-orthogonal dans les espaces des formes différentielles homogènes." Thesis, Reims, 2016. http://www.theses.fr/2016REIMS035/document.

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Dans cette thèse nous étudions des représentations du groupe de Lorentz dans les sections du fibré cotangent sur le cône isotrope. Grâce aux transformations de Fourier et de Poisson nous construisons explicitement tous les opérateurs de brisure de symétrie qui apparaissent dans les lois de branchement des produits tensoriels de telles représentations<br>In this thesis we study representations of the Lorentz group acting on sectionsof the cotangent bundle over the isotropic cone. Using Fourier and Poisson transforms we construct explicitly all the symmetry breaking operators that appear in bran

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32

Fairley, Jason Thomas. "Induced linear representations for doubly transitive groups." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.404812.

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33

Forrester-Barker, Magnus. "Representations of crossed modules and catÂ¹-groups." Thesis, Bangor University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401882.

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34

Magson, Christopher. "Real projective representations of some finite groups." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236595.

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35

AFONSO, LUIS FERNANDO CROCCO. "REPRESENTATIONS OF TRIANGLE GROUPS IN COMPLEX HYPERBOLIC." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4123@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>O principal objetivo deste trabalho é o estudo de representações que preservam tipo rho:Gamma - PU(2,1) de grupos triangulares Gamma no grupo de isometrias holomorfas do espaço hiperbólico complexo de dimensão dois H2C. O grupo triangular Gamma(p,q,r) é o grupo gerado por reflexões nos lados de um triângulo geodésico, com ângulos pi/p, pi/q e pi/r, no plano hiperbólico. Neste trabalho, nossas atenções são voltadas para os grupos Gamma (4,4,infinito) e Gamma(4,infinito,infinito). Demonstramos, entre outros resultados: Par

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36

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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37

Almutairi, Bander Nasser. "Counting supercuspidal representations of p-adic groups." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/48008/.

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Let F be a non-archimedean local �eld with residual characteristic p ~= 2. In this thesis we will deduce a formula for the number of irreducible supercuspidal representations of GLN(F), N C 1, with !�($F ) = 1 and level less than or equal to k. Following Blasco, we construct all irreducible supercuspidal representations of the unitary groups U(1; 1)(F~F0) and U(2; 1)(F~F0) by looking at their characteristic polynomials and then compute the number of all these representations according to their level.

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38

Mazhar, Siddiqua. "Composition of permutation representations of triangle groups." Thesis, University of Newcastle upon Tyne, 2017. http://hdl.handle.net/10443/3857.

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A triangle group is denoted by (p, q, r) and has finite presentation (p, q, r) = hx, y|xp = yq = (xy)r = 1i. In the 1960’s Higman conjectured that almost every triangle group has among its homomorphic images all but finitely many of the alternating groups. This was proved by Everitt in [6]. In this thesis, we combine permutation representations using the methods used in the proof of Higman’s conjecture. We do some experiments by using GAP code and then we examine the situations where the composition of a number of coset diagrams for a triangle group is imprimitive. Chapter 1 provides the intro

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39

Hendriksen, Michael Arent. "Minimal Permutation Representations of Classes of Semidirect Products of Groups." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14353.

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Given a finite group $G$, the smallest $n$ such that $G$ embeds into the symmetric group $S_n$ is referred to as the minimal degree. Much of the accumulated literature focuses on the interplay between minimal degrees and direct products. This thesis extends this to cover large classes of semidirect products. Chapter 1 provides a background for minimal degrees - stating and proving a number of essential theorems and outlining relevant previous work, along with some small original results. Chapter 2 calculates the minimal degrees for an infinite class of semidirect products - specifically the se

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40

Amende, Bonnie. "G-irreducible subgroups of type A₁ /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190506.

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Thesis (Ph. D.)--University of Oregon, 2005.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaf 152). Also available for download via the World Wide Web; free to University of Oregon users.

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41

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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42

Hua, Jiuzhao Mathematics &amp Statistics Faculty of Science UNSW. "Representations of quivers over finite fields." Awarded by:University of New South Wales. Mathematics & Statistics, 1998. http://handle.unsw.edu.au/1959.4/40405.

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The main purpose of this thesis is to obtain surprising identities by counting the representations of quivers over finite fields. A classical result states that the dimension vectors of the absolutely indecomposable representations of a quiver ?? are in one-to-one correspondence with the positive roots of a root system ??, which is infinite in general. For a given dimension vector ?? ??? ??+, the number A??(??, q), which counts the isomorphism classes of the absolutely indecomposable representations of ?? of dimension ?? over the finite field Fq, turns out to be a polynomial in q with integer

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43

Steel, Allan Kenneth. "Construction of ordinary irreducible representations of finite groups." Thesis, The University of Sydney, 2012. http://hdl.handle.net/2123/20307.

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44

Knezevic, Marica. "Graphs of lattices in representations of finite groups." Thesis, King's College London (University of London), 2017. https://kclpure.kcl.ac.uk/portal/en/theses/graphs-of-lattices-in-representations-of-finite-groups(2f435ed5-4a11-4d45-ae2b-26e3c6264ee8).html.

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This thesis work is motivated by the Langlands program, which relates objects from number theory and representation theory. In particular it is motivated by the compatibility of the local and global cases, especially in the mod p case. Given a finite group G, E a finite extension of Qp with ring of integers OE, uniformizer E, V a finite dimensional E-vector space and : G ! AutE(V ) an absolutely irreducible representation, we associate to the following directed graph: its vertices are homothety classes of lattices in V and there is an edge from (the class of) to 0 when E 0 and the quotient =0

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45

Brau, Julio. "Selmer groups of elliptic curves and Galois representations." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708896.

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46

Balagović, Martina. "On representations of quantum groups and Cherednik algebras." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/68478.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 245-248).<br>In the first part of the thesis, we study quantum groups associated to a semisimple Lie algebra g. The classical Chevalley theorem states that for [ a Cartan subalgebra and W the Weyl group of g, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials on , Res: C[g]1 -+ C[]w. A recent generalization of [36] to the case when the target space C of the polynomial maps is

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47

Roth, Calvin L. (Calvin Lee). "Example of solvable quantum groups and their representations." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28104.

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48

Wassink, Luke Samuel. "Split covers for certain representations of classical groups." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1929.

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Let R(G) denote the category of smooth representations of a p-adic group. Bernstein has constructed an indexing set B(G) such that R(G) decomposes into a direct sum over s ∈ B(G) of full subcategories Rs(G) known as Bernstein subcategories. Bushnell and Kutzko have developed a method to study the representations contained in a given subcategory. One attempts to associate to that subcategory a smooth irreducible representation (τ,W) of a compact open subgroup J < G. If the functor V ↦ HomJ(W,V) is an equivalence of categories from Rs(G) → H(G,τ)mod we call (J,τ) a type. Given a Levi subgroup L

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49

Fitzpatrick, Michael Colin. "Continuous families of representations of mapping class groups." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1316.

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The study of mapping class groups began in the 1920s with Max Dehn and Jakob Nielsen. It was about this time that topology was just being developed, so mapping class groups were of immediate interest, being invariants of topological spaces. The works of Dehn and Nielsen were continued by William Harvey in the 1960s and 70s leading to the development of the curve complex, an important construction still very relevant to mathematics today. William Thurston is another important name in this area since he was able to completely classify homeomorphisms of surfaces in 1976, leading to the famous "Ni

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50

Schoemann, Claudia. "Représentations unitaires de U(5) p-adique." Thesis, Montpellier 2, 2014. http://www.theses.fr/2014MON20101.

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Nous étudions les représentations complexes, induites par l'induction parabolique, du groupe U(5), défini sur un corps local non-archimedean de caractéristique 0. C'est Qp ou une extension finie de Qp .On parle des 'corps p-adiques'. Soit F un corps p-adique. Soit E : F une extension de corps de degré 2. Soit Gal(E : F ) = {id, σ}le groupe de Galois. On écrit σ(x) = overline{x} forall x ∈ E. Soit | |p la norme p-adique de E. Soient E* = E {0} et E 1 = {x ∈ E | xoverline{x}= 1} .U (5) a trois sous-groupes paraboliques propres. Soit P0 le sous-groupe parabolique minimal et soientP1 et P2 les deu

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