Representation Theory of Finite Reductive Groups

by Marc Cabanes, Michel Enguehard

Overview

At the crossroads of representation theory, algebraic geometry and finite group theory, this book brings together many of the main concerns of modern algebra, synthesizing the past twenty-five years of research, by including some of the most remarkable achievements in the field. The text is illustrated throughout by many examples, and background material is provided by several introductory chapters on basic results as well as appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and a reference for all algebraists.

Product Details

ISBN-13:	9780521825177
Publisher:	Cambridge University Press
Publication date:	01/29/2004
Series:	New Mathematical Monographs , #1
Pages:	456
Product dimensions:	5.98(w) x 9.02(h) x 1.14(d)

Table of Contents

Introduction; Notations and conventions; Part I. Representing Finite BN-Pairs: 1. Cuspidality in finite groups; 2. Finite BN-pairs; 3. Modular Hecke algebras for finite BN-pairs; 4. Modular duality functor and the derived category; 5. Local methods for the transversal characteristics; 6. Simple modules in the natural characteristic; Part II. Deligne–Lusztig Varieties, Rational Series, and Morita Equivalences: 7. Finite reductive groups and Deligne–Lusztig varieties; 8. Characters of finite reductive groups; 9. Blocks of finite reductive groups and rational series; 10. Jordan decomposition as a Morita equivalence, the main reductions; 11. Jordan decomposition as a Morita equivalence, sheaves; 12. Jordan decomposition as a Morita equivalence, modules; Part III. Unipotent Characters and Unipotent Blocks: 13. Levi subgroups and polynomial orders; 14. Unipotent characters as a basic set; 15. Jordan decomposition of characters; 16. On conjugacy classes in type D; 17. Standard isomorphisms for unipotent blocks; Part IV. Decomposition Numbers and q-Schur Algebras: 18. Some integral Hecke algebras; 19. Decomposition numbers and q-Schur algebras, general linear groups; 20. Decomposition numbers and q-Schur algebras, linear primes; Part V. Unipotent Blocks and Twisted Induction: 21. Local methods. Twisted induction for blocks; 22. Unipotent blocks and generalized Harish Chandra theory; 23. Local structure and ring structure of unipotent blocks; Appendix 1: Derived categories and derived functors; Appendix 2: Varieties and schemes; Appendix 3: Etale cohomology; References; Index.

Editorial Reviews

'This monograph treats the representation theory of finite reductive groups mostly in transversal characteristic, i.e. in a characteristic that differs from the natural characteristic p of the group.' Zentralblatt MATH

From the Publisher