Representations of Hecke Algebras at Roots of Unity

  • Meinolf Geck
  • Nicolas Jacon

Part of the Algebra and Applications book series (AA, volume 15)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Meinolf Geck, Nicolas Jacon
    Pages 1-58
  3. Meinolf Geck, Nicolas Jacon
    Pages 59-132
  4. Meinolf Geck, Nicolas Jacon
    Pages 133-206
  5. Meinolf Geck, Nicolas Jacon
    Pages 207-259
  6. Meinolf Geck, Nicolas Jacon
    Pages 261-307
  7. Meinolf Geck, Nicolas Jacon
    Pages 309-361
  8. Meinolf Geck, Nicolas Jacon
    Pages 363-386
  9. Back Matter
    Pages 387-401

About this book

Introduction

The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.

Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras.

The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.

This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.

Keywords

Canonical bases Fock spaces Hecke algebras Modular representations

Authors and affiliations

  • Meinolf Geck
    • 1
  • Nicolas Jacon
    • 2
  1. 1.King's College, Department of Mathematical SciencesUniversity of AberdeenAberdeenUnited Kingdom
  2. 2.UFR Sciences et TechniquesUniversité de Franche-ComtéBesanconFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-716-7
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-715-0
  • Online ISBN 978-0-85729-716-7
  • About this book