Modular Representations of Finite Groups of Lie Type
1st Edition
Published on 19. January 2011
978-0-511-89387-2 (ISBN)
Description
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.
Reviews / Votes
'This is the first comprehensive treatment of the representation theory of finate groups of Lie type over a field of the defining prime charecteristic.' L'enseignement mathematiqueMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 30 Tables, unspecified; 30 Plates, unspecified
File size
2,38 MB
ISBN-13
978-0-511-89387-2 (9780511893872)
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Schweitzer Classification
Other editions
Additional editions
James E. Humphreys
Modular Representations of Finite Groups of Lie Type
Book
12/2005
Cambridge University Press
€92.30
Shipment within 15-20 days
Person
James E. Humphreys was born in Erie, Pennsylvania, and received his AB from Oberlin College, Ohio in 1961, and his PhD from Yale University, Connecticut in 1966. He has taught at the University of Oregon, Courant Institute of Mathematical Sciences, New York University, and the University of Massachusetts, Amherst (now retired). He visits the Institute of Advanced Studies, Princeton and Rutgers. He is the author of several graduate texts and monographs.
Content
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.
