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Representations of General Linear Groups : Cambridge Economic Handbooks - G.D. James

Representations of General Linear Groups

Cambridge Economic Handbooks

Paperback Published: 23rd July 1984
ISBN: 9780521269810
Number Of Pages: 160

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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.

Introduction
Examples
Gaussian polynomials
Compositions of n
Root subgroups of Gn
Subgroups of Gn associated with compositions
Coset representatives
Subgroups of Gn used for induction
Some idempotent elements of KGn
The permutation module M
The Submodule Theorem
A lower bound for the dimension of Su
The Kernel Intersection Theorem for S (n-m,m)
Reordering the parts of X
The Kernel Intersection Theorem
Consequences of the Kernel Intersection Theorem
Removing the first column from [X]
Isotropic spaces
The prime divisors of Gaussian polynomials
The composition factors of S (n-m,m)
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521269810
ISBN-10: 0521269814
Series: Cambridge Economic Handbooks
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 160
Published: 23rd July 1984
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 0.94
Weight (kg): 0.25

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