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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.Read more
- 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
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- Date Published: January 2006
- format: Paperback
- isbn: 9780521674546
- length: 248 pages
- dimensions: 229 x 153 x 15 mm
- weight: 0.34kg
- contains: 30 tables
- availability: 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
9. Projective modules
10. Comparison with Frobenius kernels
11. Cartan invariants
12. Extensions of simple modules
13. Loewy series
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
Frequently used symbols
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