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Kazhdan-Lusztig Cells with Unequal Parameters

  • Cédric Bonnafé

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
    3. Cédric Bonnafé
      Pages 189-199
  7. Applications of Lusztig’s Conjectures

    1. Front Matter
      Pages 201-203
    2. Cédric Bonnafé
      Pages 205-208
    3. Cédric Bonnafé
      Pages 209-217
    4. Cédric Bonnafé
      Pages 219-224
    5. Cédric Bonnafé
      Pages 225-233
    6. Cédric Bonnafé
      Pages 235-240
  8. Examples

    1. Front Matter
      Pages 241-242
    2. Cédric Bonnafé
      Pages 243-262
    3. Cédric Bonnafé
      Pages 263-271
    4. Cédric Bonnafé
      Pages 273-279
    5. Cédric Bonnafé
      Pages 281-301
    6. Cédric Bonnafé
      Pages 303-317
    7. Cédric Bonnafé
      Pages 319-321
  9. Back Matter
    Pages 323-348

About this book

Introduction

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.

Keywords

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

  • Cédric Bonnafé
    • 1
  1. 1.Institut Montpelliérain Alexander GrothendieckCNRS-Université de MontpellierMontpellierFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70736-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70735-8
  • Online ISBN 978-3-319-70736-5
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site