Representations of Reductive Groups

This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.

Roger W. Carter (Edited by), Meinolf Geck (Edited by)

9780521643252, Cambridge University Press

Hardback, published 3 September 1998

200 pages, 12 b/w illus.
23.6 x 15.6 x 1.6 cm, 0.4 kg

"It seems doubtful that a group of outstanding experts manages it to write survey articles which are carefully coordinated and support eachother. This book proves impressively the practicability of such a project..." Monatshefte fur Math

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.

Subject Areas: Groups & group theory [PBG]