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Representations of Reductive Groups (Publications of the Newton Institute)

Representations of Reductive Groups (Publications of the Newton Institute)

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Meinolf Geck Edited by Roger W. Carter
Cambridge University Press, 9/3/1998
EAN 9780521643252, ISBN10: 0521643252

Hardcover, 200 pages, 22.9 x 15.8 x 2.3 cm
Language: English

The representation theory of reductive algebraic groups and related finite reductive groups is a subject of great topical interest and has many applications. The articles in this volume provide introductions to various aspects of the subject, including algebraic groups and Lie algebras, reflection groups, abelian and derived categories, the Deligne-Lusztig representation theory of finite reductive groups, Harish-Chandra theory and its generalisations, quantum groups, subgroup structure of algebraic groups, intersection cohomology, and Lusztig's conjectured character formula for irreducible representations in prime characteristic. The articles are carefully designed to reinforce one another, and are written by a team of distinguished authors: M. Broué, R. W. Carter, S. Donkin, M. Geck, J. C. Jantzen, B. Keller, M. W. Liebeck, G. Malle, J. C. Rickard and R. Rouquier. This volume as a whole should provide a very accessible introduction to an important, though technical, subject.

1. Introduction to algebraic groups and Lie algebras R. W. Carter
2. Weyl groups, affine Weyl groups, and reflection groups R. Rouquier
3. Introduction to abelian and derived categories B. Keller
4. Finite groups of Lie type M. Geck
5. Generalized Harish-Chandra theory M. Broue and G. Malle
6. Introduction to quantum groups J. C. Jantzen
7. Introduction to the subgroup structure of algebraic groups M. W. Liebeck
8. Introduction to intersection cohomology J. Rickard
9. Introduction to Lusztig's Conjecture S. Donkin.