Modular representations of finite groups of Lie type / James E. Humphreys.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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. groups G[subscript 2](q) -- 19. General and special linear groups -- 20. Suzuki and Ree groups.

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.