© 2017

Kazhdan-Lusztig Cells with Unequal Parameters

  • Provides a self-contained introduction to Kazhdan-Lusztig cells

  • Includes figures of the partition into cells for small finite, affine, or hyperbolic Coxeter groups

  • Explains Geck and Guilhot induction results, as well as the action of the cactus group

  • Reviews and adds substantial results to an active field of research


Part of the Algebra and Applications book series (AA, volume 24)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Preliminaries

    1. Front Matter
      Pages 1-2
    2. Cédric Bonnafé
      Pages 3-11
    3. Cédric Bonnafé
      Pages 13-16
  3. Coxeter Systems, Hecke Algebras

    1. Front Matter
      Pages 17-18
    2. Cédric Bonnafé
      Pages 19-51
    3. Cédric Bonnafé
      Pages 53-69
  4. Kazhdan–Lusztig Cells

    1. Front Matter
      Pages 71-72
    2. Cédric Bonnafé
      Pages 73-91
    3. Cédric Bonnafé
      Pages 93-110
    4. Cédric Bonnafé
      Pages 111-115
  5. General Properties of Cells

    1. Front Matter
      Pages 117-118
    2. Cédric Bonnafé
      Pages 119-131
    3. Cédric Bonnafé
      Pages 133-137
    4. Cédric Bonnafé
      Pages 147-153
    5. Cédric Bonnafé
      Pages 155-168
    6. Cédric Bonnafé
      Pages 169-172
  6. Lusztig’s a-Function

    1. Front Matter
      Pages 173-174
    2. Cédric Bonnafé
      Pages 175-188

About this book


This monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case.

Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal work on the subject was published in 2002. The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group.

Kazhdan-Lusztig Cells with Unequal Parameters will appeal to graduate students and researchers interested in related subject areas, such as Lie theory, representation theory, and combinatorics of Coxeter groups. Useful examples and various exercises make this book suitable for self-study and use alongside lecture courses.


MSC (2010): 20C08, 20F55 Coxeter groups Hecke algebras with unequal parameters Kazhdan Lusztig cells cellular maps group theory Lusztig's $a$-function Lusztig conjectures Lusztig conjectures applications Kazhdan-Lusztig cells cells and parabolic subgroups submaximal cells

Authors and affiliations

  1. 1.Institut Montpelliérain Alexander GrothendieckCNRS-Université de MontpellierMontpellierFrance

About the authors

Cédric Bonnafé is an expert in representation theory of finite reductive groups and related objects (such as Hecke algebras or rational Cherednik algebras). He is the author of several papers on the Kazhdan-Lusztig theory of cells.

Bibliographic information

  • Book Title Kazhdan-Lusztig Cells with Unequal Parameters
  • Authors Cédric Bonnafé
  • Series Title Algebra and Applications
  • Series Abbreviated Title Algebra, Applications
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-70735-8
  • Softcover ISBN 978-3-030-09986-2
  • eBook ISBN 978-3-319-70736-5
  • Series ISSN 1572-5553
  • Series E-ISSN 2192-2950
  • Edition Number 1
  • Number of Pages XXV, 348
  • Number of Illustrations 13 b/w illustrations, 15 illustrations in colour
  • Topics Group Theory and Generalizations
  • Buy this book on publisher's site