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EBOOK
Author Humphreys, James E.
Title Modular representations of finite groups of Lie type / James E. Humphreys.
Imprint Cambridge, UK ; New York : Cambridge University Press, 2006.

Series London Mathematical Society lecture note series ; 326
London Mathematical Society lecture note series ; 326.
Subject Modular representations of groups.
Representations of Lie groups.
Finite simple groups.
Alt Name London Mathematical Society.
Description 1 online resource (xv, 233 pages) : illustrations.
Bibliography Note Includes bibliographical references (pages 213-228) and index.
Note Print version record.
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. groups G[subscript 2](q) -- 19. General and special linear groups -- 20. Suzuki and Ree groups.
Summary 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.
ISBN 9781107362802 (electronic bk.)
1107362806 (electronic bk.)
0521674549
9780521674546
OCLC # 836848765
Additional Format Print version: Humphreys, James E. Modular representations of finite groups of Lie type. Cambridge, UK ; New York : Cambridge University Press, 2006 0521674549 (DLC) 2006276125 (OCoLC)61757066