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Introduction to Soergel Bimodules

  • Ben Elias
  • Shotaro Makisumi
  • Ulrich Thiel
  • Geordie Williamson
Book

Part of the RSME Springer Series book series (RSME, volume 5)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. The Classical Theory of Soergel Bimodules

    1. Front Matter
      Pages 1-1
    2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 3-23
    3. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 25-37
    4. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 39-58
    5. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 59-75
    6. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 77-97
    7. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 99-116
  3. Diagrammatic Hecke Category

    1. Front Matter
      Pages 117-117
    2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 119-131
    3. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 133-150
    4. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 151-166
    5. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 167-199
    6. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 201-238
    7. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 239-256
  4. Historical Context: Category O $$\mathcal {O}$$ and the Kazhdan–Lusztig Conjectures

    1. Front Matter
      Pages 257-257
    2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 259-269
    3. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 271-292
    4. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 293-313
    5. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 315-331
  5. The Hodge Theory of Soergel Bimodules

    1. Front Matter
      Pages 333-333
    2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 335-346
    3. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 347-367
    4. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 369-399
    5. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 401-418
  6. Special Topics

    1. Front Matter
      Pages 419-419
    2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 421-440
    3. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 441-459
    4. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 461-480
    5. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 481-512
    6. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 513-527
    7. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 529-548
    8. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
      Pages 549-569
  7. Back Matter
    Pages 571-588

About this book

Introduction

This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research.

This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.



Keywords

Soergel bimodules Representation theory Kazhdan-Lusztig conjecture Kazhdan-Lusztig polynomials Higher representation theory

Authors and affiliations

  • Ben Elias
    • 1
  • Shotaro Makisumi
    • 2
  • Ulrich Thiel
    • 3
  • Geordie Williamson
    • 4
  1. 1.Department of MathematicsUniversity of Oregon, Fenton HallEugeneUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA
  3. 3.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  4. 4.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

Bibliographic information