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Book Cover
E-book
Author Humphreys, James E

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

Copies

Description 1 online resource (xv, 233 pages) : illustrations
Series London Mathematical Society lecture note series ; 326
London Mathematical Society lecture note series ; 326.
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
Bibliography Includes bibliographical references (pages 213-228) and index
Notes English
Print version record
Subject Modular representations of groups.
Representations of Lie groups.
Finite simple groups.
MATHEMATICS -- Group Theory.
Finite simple groups
Modular representations of groups
Representations of Lie groups
Eindige groepen.
Lie-groepen.
Form Electronic book
Author London Mathematical Society.
ISBN 9781107362802
1107362806
1139882538
9781139882538
1107367719
9781107367715
1107372259
9781107372252
1107370043
9781107370043
1299405312
9781299405318
1107365252
9781107365254