Progress in Mathematics

D-Modules, Perverse Sheaves, and Representation Theory

Authors: Hotta, Ryoshi, Takeuchi, Kiyoshi, Tanisaki, Toshiyuki

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  • The unique text treating an algebraic-analytic approach to D-module theory
  • Examines D-module theory, connecting algebraic geometry and representation theory
  • Detailed examination with excellent proof of the Riemann-Hilbert correspondence
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-0-8176-4523-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-0-8176-4363-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

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)


Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-0-8176-4523-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-0-8176-4363-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
D-Modules, Perverse Sheaves, and Representation Theory
Authors
Translated by
Takeuchi, K.
Series Title
Progress in Mathematics
Series Volume
236
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4523-6
DOI
10.1007/978-0-8176-4523-6
Hardcover ISBN
978-0-8176-4363-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XI, 412
Topics