Finite Reductive Groups: Related Structures and Representations

Proceedings of an International Conference held in Luminy, France

  • Marc Cabanes

Part of the Progress in Mathematics book series (PM, volume 141)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Susumi Ariki
    Pages 1-13
  3. Anne-Marie Aubert
    Pages 15-49
  4. Christine Bessenrodt, Jørn B. Olsson
    Pages 51-71
  5. Marc Cabanes, Michel Enguehard
    Pages 141-163
  6. Arjeh M. Cohen, Pham Huu Tiep
    Pages 165-183
  7. Charles W. Curtis, Toshiaki Shoji
    Pages 185-194
  8. Meinolf Geck, Raphaël Rouquier
    Pages 251-272
  9. Lluis Puig
    Pages 361-372
  10. Marie-France Vignéras
    Pages 415-452

About this book

Introduction

Finite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the subject was revolutionized by the introduction of constructions from l-adic cohomology by Deligne-Lusztig (1976) and by the approach of character-sheaves by Lusztig (1985). The theory now also incorporates the methods of Brauer for the linear representations of finite groups in arbitrary characteristic and the methods of representations of algebras. It has become one of the most active fields of contemporary mathematics.

The present volume reflects the richness of the work of experts gathered at an international conference held in Luminy. Linear representations of finite reductive groups (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular aspects Cabanes Enguehard, Geck-Hiss) go side by side with many related structures: Hecke algebras associated with Coxeter groups (Ariki, Geck-Rouquier, Pfeiffer), complex reflection groups (Broué-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vignéras), Lie groups (Cohen-Tiep), symmetric groups (Bessenrodt-Olsson), and general finite groups (Puig). With the illuminating introduction by Paul Fong, the present volume forms the best invitation to the field.

Keywords

Algebra Arithmetic Finite Group theory Mathematics Morphism Reductive Groups function

Editors and affiliations

  • Marc Cabanes
    • 1
  1. 1.UFR de MathématiquesUniversité Paris VIICedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4124-9
  • Copyright Information Birkhäuser Boston 1997
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8664-6
  • Online ISBN 978-1-4612-4124-9
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book