Modular Representations of Finite Groups of Lie Type

A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

James E. Humphreys (Author)

9780521674546, Cambridge University Press

Paperback, published 22 December 2005

248 pages, 30 tables
22.9 x 15.3 x 1.5 cm, 0.34 kg

'This is the first comprehensive treatment of the representation theory of finate groups of Lie type over a field of the defining prime charecteristic.' L'enseignement mathematique

Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne–Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.

1. Finite groups of Lie type
2. Simple modules
3. Weyl modules and Lusztig's conjecture
4. Computation of weight multiplicities
5. Other aspects of simple modules
6. Tensor products
7. BN-pairs and induced modules
8. Blocks
9. Projective modules
10. Comparison with Frobenius kernels
11. Cartan invariants
12. Extensions of simple modules
13. Loewy series
14. Cohomology
15. Complexity and support varieties
16. Ordinary and modular representations
17. Deligne-Lusztig characters
18. The groups G2
19. General and special linear groups
20. Suzuki and Ree groups
Bibliography
Frequently used symbols
Index.

Subject Areas: Groups & group theory [PBG], Algebra [PBF]