Modular Representations of Finite Groups of Lie Type
Modular Representations of Finite Groups of Lie Type
$83.99
USDFinite 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.
- This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic
- Core material is covered in detail, while other topics and recent developments are surveyed
- One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology: chapters are accompanied by examples and carefully selected references
Reviews & endorsements
"In addition to being a leader in the field of modular representation theory, Humphreys' clarity of exposition is almost universally known. The book is expertly written...Humphreys has done a great service to the representation-theoretic community by writing this book."
John Cullinan, MAA Reviews, MathDL
Product details
January 2006Paperback
9780521674546
248 pages
229 × 153 × 15 mm
0.34kg
30 tables
Available
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.
