Synopses & Reviews
Comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Synopsis
Finite groups of Lie type encompass most of the finite simple groups. Their matrix 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. The aim here is to make the subject more accessible to researchers in neighboring parts of group theory, number theory, and topology.
About the Author
James E. Humphreys is a Retired Professor at the Department of Mathematics, University of Massachusetts.
Table of Contents
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.