Representation Theory of Finite Reductive Groups

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.