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

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Published: 4 June 2021

Last updated: 28 July 2025

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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

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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

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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5

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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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

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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

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 o

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11

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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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

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17

ARAGONA, RICCARDO. "Semi-invariants of symmetric quivers." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/1104.

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L'obiettivo della tesi è descrivere l'anello dei semi-invarianti di quiver simmetrici di tipo finito e di tipo tame. Nella prima parte dimostriamo risultati generali riguardanti i semi-invarinti di quiver simmetrici. Poi enunciamo e dimostriamo il teorema centrale in cui esibiamo un insieme di generatori dell'anello dei semi-invarianti di quiver simmetrici di tipo finito e di tipo tame. Congetturiamo vero infine questo teorema per qualsiasi quiver simmetrico.<br>The goal of the thesis is to describe the ring of semi-invariants for symmetric quivers of finite and tame type. First, we prove gene

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18

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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19

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 c

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20

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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21

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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22

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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23

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

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24

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 ma

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25

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 comp

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26

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 stabl

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27

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 i

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28

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 certaine

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29

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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30

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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31

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 class

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32

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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33

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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34

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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35

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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36

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 result

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37

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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38

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

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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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40

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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41

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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42

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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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 te

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44

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 realiza

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45

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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46

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 combi

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47

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 algeb

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48

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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49

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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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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Abstract:

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 représent

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