Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 236)
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Table of contents (13 chapters)
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Front Matter
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D-Modules and Perverse Sheaves
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Front Matter
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Back Matter
Keywords
About this book
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)
Editors and Affiliations
Bibliographic Information
Book Title: D-Modules, Perverse Sheaves, and Representation Theory
Editors: Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-0-8176-4523-6
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Boston 2008
Hardcover ISBN: 978-0-8176-4363-8Published: 07 November 2007
eBook ISBN: 978-0-8176-4523-6Published: 12 October 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XI, 412
Number of Illustrations: 1 b/w illustrations
Topics: Algebra, Group Theory and Generalizations, Topological Groups, Lie Groups, Commutative Rings and Algebras, Algebraic Geometry