Modular representations of finite groups of Lie type
著者
書誌事項
Modular representations of finite groups of Lie type
（London Mathematical Society lecture note series, 326）
Cambridge University Press, 2006, c2005
- : pbk
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注記
Includes bibliographical references (p. 213-228) and index
内容説明・目次
内容説明
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.
目次
- 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.
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