Modular Representations of Finite Groups of Lie Type

ISBN-13: 9780521674546 / Angielski / Miękka / 2006 / 248 str.

J. E. Humphreys; N. J. Hitchin

Opis

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 neighboring parts of group theory, number theory, and topology.

Recenzje

'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

Spis treści

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.