© 2011

Representations of SL2(Fq)

  • Presents an introduction to ordinary and modular Deligne-Lusztig theory through the detailed study of an example: SL2(Fq)

  • Will serve as a complimentary text to existing titles on Deligne-Lusztig theory

  • Includes Rouquier's theorem on derived equivalences of geometric nature (with some unpublished improvements) but is simple enough to be read by graduate/Ph. D. students


Part of the Algebra and Applications book series (AA, volume 13)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Preliminaries

    1. Front Matter
      Pages 1-2
    2. Cédric Bonnafé
      Pages 15-25
  3. Ordinary Characters

    1. Front Matter
      Pages 27-28
    2. Cédric Bonnafé
      Pages 29-35
    3. Cédric Bonnafé
      Pages 37-50
    4. Cédric Bonnafé
      Pages 51-58
  4. Modular Representations

    1. Front Matter
      Pages 59-61
    2. Cédric Bonnafé
      Pages 71-84
    3. Cédric Bonnafé
      Pages 109-126
  5. Complements

    1. Front Matter
      Pages 127-128
    2. Cédric Bonnafé
      Pages 129-148
    3. Cédric Bonnafé
      Pages 149-157
  6. Back Matter
    Pages 159-186

About this book


Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provide the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects.

The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups.

At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.


Deligne-Lusztig theory Morita equivalences SL(2, q) characters derived equivalences modular representations nite reductive groups

Authors and affiliations

  1. 1.Universite Montpellier 2, Institut de Math et de ModélisationCNRS (UMR 5149)MONTPELLIER CedexFrance

Bibliographic information