Representations of General Linear Groups

by G. D. James

Overview

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.

Product Details

ISBN-13:	9780521269810
Publisher:	Cambridge University Press
Publication date:	05/24/1984
Series:	London Mathematical Society Lecture Note Series , #94
Edition description:	New Edition
Pages:	160
Product dimensions:	5.98(w) x 9.02(h) x 0.35(d)

Table of Contents

Abstract; List of symbols; 1. Introduction; 2. Examples; 3. Gaussian polynomials; 4. Compositions of n; 5. Root subgroups of Gn; 6. Subgroups of Gn associated with compositions; 7. Coset representatives; 8. Subgroups of Gn used for induction; 9. Some idempotent elements of KGn; 10. The permutation module Mλ; 11. The Submodule Theorem; 12. A lower bound for the dimension of Sμ; 13. The Kernel Intersection Theorem for S(n-m,m); 14. Reordering the parts of λ; 15. The Kernel Intersection Theorem; 16. Consequences of the Kernel Intersection Theorem; 17. Removing the first column from [λ]; 18. Isotropic spaces; 19. The prime divisors of Gaussian polynomials; 20. The composition factors of S(n-m,m); Acknowledgements; References.