Representations of Reductive Groups

doi:10.1017/CBO9780511600623

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.

"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

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction to algebraic groups and Lie algebras
pp 1-20

Weyl groups, affine Weyl groups and reflection groups
pp 21-40

Introduction to abelian and derived categories
pp 41-62

Finite groups of Lie type
pp 63-84

Generalized Harish-Chandra theory
pp 85-104

Introduction to quantum groups
pp 105-128

Introduction to the subgroup structure of algebraic groups
pp 129-150

Introduction to intersection cohomology
pp 151-172

An introduction to the Lusztig Conjecture
pp 173-188

Index
pp 189-191

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