Representations of General Linear Groups

G. D. James

doi:10.1017/CBO9780511661921

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Dipper, Richard 1985. On the decomposition numbers of the finite general linear groups. II. Transactions of the American Mathematical Society, Vol. 292, Issue. 1, p. 123.

CrossRef

Google Scholar

Kostrikin, A. I. and Chubarov, I. A. 1988. Representations of finite groups. Journal of Soviet Mathematics, Vol. 40, Issue. 3, p. 331.

CrossRef

Google Scholar

Frumkin, Avital and Yakir, Arieh 1990. Rank of inclusion matrices and modular representation theory. Israel Journal of Mathematics, Vol. 71, Issue. 3, p. 309.

CrossRef

Google Scholar

Dipper, Richard 1991. Representation Theory of Finite Groups and Finite-Dimensional Algebras. p. 343.

CrossRef

Google Scholar

Maslen, David and Rockmore, Daniel 1997. Separation of variables and the computation of Fourier transforms on finite groups, I. Journal of the American Mathematical Society, Vol. 10, Issue. 1, p. 169.

CrossRef

Google Scholar

Bleher, Frauke M. Kimmerle, Wolfgang Roggenkamp, Klaus W. and Wursthor, Martin 1999. Algorithmic Algebra and Number Theory. p. 313.

CrossRef

Google Scholar

Mnukhin, V.B. and Siemons, I.J. 2000. On modular homology in projective space. Journal of Pure and Applied Algebra, Vol. 151, Issue. 1, p. 51.

CrossRef

Google Scholar

Orrison, Michael E. 2004. Radon transforms and the finite general linear groups. Forum Mathematicum, Vol. 16, Issue. 1,

CrossRef

Google Scholar

Fayers, Matthew 2005. q-Schur Subalgebras. Algebras and Representation Theory, Vol. 8, Issue. 3, p. 415.

CrossRef

Google Scholar

Lyle, Sinéad and Mathas, Andrew 2005. Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules. Journal of Algebraic Combinatorics, Vol. 22, Issue. 2, p. 151.

CrossRef

Google Scholar

ACKERMANN, BERND and SCHROLL, SIBYLLE 2007. On decomposition numbers and Alvis–Curtis duality. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 143, Issue. 3, p. 509.

CrossRef

Google Scholar

Hertweck, Martin and Soriano, Marcos 2007. Parametrization of central Frattini extensions and isomorphisms of small group rings. Israel Journal of Mathematics, Vol. 157, Issue. 1, p. 63.

CrossRef

Google Scholar

Reiner, Victor and Stanton, Dennis 2010. (q,t)-analogues and $GL_{n}({\mathbb{F}}_{q})$. Journal of Algebraic Combinatorics, Vol. 31, Issue. 3, p. 411.

CrossRef

Google Scholar

Siemons, J. and Smith, D. 2014. Some Homology Representations for Grassmannians in Cross-Characteristics. Journal of Mathematical Sciences, Vol. 199, Issue. 3, p. 329.

CrossRef

Google Scholar

Mínguez, Alberto and Sécherre, Vincent 2014. Représentations lisses modulo ℓ de GLm(D). Duke Mathematical Journal, Vol. 163, Issue. 4,

CrossRef

Google Scholar

Sécherre, Vincent and Venketasubramanian, Coolimuttam G. 2016. Modular Representations of ${\rm GL}{(n)}$ Distinguished by ${\rm GL}{(n-1)}$ over a $p$-Adic Field. International Mathematics Research Notices, p. rnw150.

CrossRef

Google Scholar

Plaza, Rafael and Xiang, Qing 2018. Resilience of ranks of higher inclusion matrices. Journal of Algebraic Combinatorics, Vol. 48, Issue. 1, p. 31.

CrossRef

Google Scholar

Andrews, Scott 2018. The unipotent modules of $${{\mathrm {GL}}}_{n}({{\mathbb {F}}}_{q})$$ GL n ( F q ) via tableaux. Journal of Algebraic Combinatorics, Vol. 47, Issue. 1, p. 1.

CrossRef

Google Scholar

DE BOECK, M. EVSEEV, A. LYLE, S. and SPEYER, L. 2018. ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS. Transformation Groups, Vol. 23, Issue. 3, p. 631.

CrossRef

Google Scholar

Danz, Susanne and Hofmann, Tommy 2019. ON LATTICES OF INTEGRAL GROUP ALGEBRAS AND SOLOMON ZETA FUNCTIONS. International Electronic Journal of Algebra, p. 129.

CrossRef

Google Scholar

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G. D. James

Publisher:: Cambridge University Press
Online publication date:: May 2010
Print publication year:: 1984
Online ISBN:: 9780511661921
DOI:: https://doi.org/10.1017/CBO9780511661921

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: London Mathematical Society Lecture Note Series (94)

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The most important examples of finite groups are the group of permutations of a set of n objects, known as the symmetric group, and the group of non-singular n-by-n matrices over a finite field, which is called the general linear group. This book examines the representation theory of the general linear groups, and reveals that there is a close analogy with that of the symmetric groups. It consists of an essay which was joint winner of the Cambridge University Adams Prize 1981-2, and is intended to be accessible to mathematicians with no previous specialist knowledge of the topics involved.Many people have studied the representations of general linear groups over fields of the natural characteristic, but this volume explores new territory by considering the case where the characteristic of the ground field is not the natural one. Not only are the results in the book elegant and interesting in their own right, but they suggest many lines for further investigation.

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Representations of General Linear Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Abstract
pp vii-ix

List of Symbols
pp x-xii

1 - Introduction
pp 1-6

2 - Examples
pp 7-17

3 - Gaussian polynomials
pp 18-19

4 - Compositions of n
pp 20-22

5 - Root subgroups of Gn
pp 23-27

6 - Subgroups of Gn associated with compositions
pp 28-29

7 - Coset representatives
pp 30-34

8 - Subgroups of Gn used for induction
pp 35-39

9 - Some idempotent elements of K̄Gn
pp 40-46

10 - The permutation module Mλ
pp 47-55

11 - The Submodule Theorem
pp 56-66

12 - A lower bound for the dimension of Sμ
pp 67-74

13 - The Kernel Intersection Theorem for S(n−m,m)
pp 75-79

14 - Reordering the parts of λ
pp 80-83

15 - The Kernel Intersection Theorem
pp 84-99

16 - Consequences of the Kernel Intersection Theorem
pp 100-108

17 - Removing the first column from [λ]
pp 109-113

18 - Isotropic spaces
pp 114-123

19 - The prime divisors of Gaussian polynomials
pp 124-135

20 - The composition factors of S(n-m,m)
pp 136-144

Acknowledgements
pp 145-145

References
pp 146-147

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Representations of General Linear Groups

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