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© 2008

D-Modules, Perverse Sheaves, and Representation Theory

  • Ryoshi Hotta
  • Kiyoshi Takeuchi
  • Toshiyuki Tanisaki

Benefits

  • D-modules a stimulating and active area of research

  • The unique text treating an algebraic-analytic approach to D-module theory

  • Examines D-module theory, connecting algebraic geometry and representation theory

  • Clusters with many Springer books written by the authors, Kashiwara, Schapira and others

  • Uses D-module theory to prove the celebrated Kazhdan-Lusztig polynomials

  • Detailed examination with excellent proof of the Riemann-Hilbert correspondence

Textbook

Part of the Progress in Mathematics book series (PM, volume 236)

Table of contents

  1. Front Matter
    Pages I-11
  2. D-Modules and Perverse Sheaves

    1. Front Matter
      Pages 13-13
    2. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 15-56
    3. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 57-80
    4. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 81-97
    5. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 99-126
    6. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 127-159
    7. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 161-170
    8. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 171-179
    9. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 181-225
  3. Representation Theory

    1. Front Matter
      Pages 227-227
    2. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 229-257
    3. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 259-270
    4. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 271-287
    5. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 289-303
    6. Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
      Pages 305-320
  4. Back Matter
    Pages 321-407

About this book

Introduction

D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory.

Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory.

To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory.

Keywords

D-Modules Hecke algebras Hodge modules Meromorphic function Representation theory algebra algebraic varieties perverse sheaves

Editors and affiliations

  • Ryoshi Hotta
    • 1
  • Kiyoshi Takeuchi
    • 2
  • Toshiyuki Tanisaki
    • 3
  1. 1.Professor Emeritus of Tohoku UniversityWako 351-0101Japan
  2. 2.School of MathematicsTsukuba UniversityTenoudai 1-1-1Japan
  3. 3.Department of Mathematics Graduate School of ScienceOsaka City UniversitySumiyoshi-kuJapan

Bibliographic information

Reviews

From the reviews:

"A self-contained introduction to D-modules, with the aim of showing how they were used to solve the Kazhdan-Lusztig conjecture. … present book can be used as a good reference on D-modules and on advanced representation theory of semisimple Lie algebras, but especially as a detailed account on the relations between them; in fact, in our opinion this is the first and very welcome complete work devoted to a mainstream research field (the ‘Algebraic Analysis’ approach to representation theory) which remains very active almost thirty years." (Corrado Marastoni, Mathematical Reviews, Issue 2008 k)

“The present book provides a reader-friendly treatment of the subject, suitable for graduate students who wish to enter the area. Part I of the book presents the theory of D-modules … . The treatment in the book is quite complete … . Part II provides the necessary background in the structure of semi-simple Lie algebras and their representations.” (Dennis Gaitsgory, Bulletin of the American Mathematical Society, Vol. 47 (4), October, 2010)