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)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
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.
Similar content being viewed by others
Table of contents (13 chapters)
-
Front Matter
-
D-Modules and Perverse Sheaves
-
Front Matter
-
-
Back Matter
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
Accessibility Information
Accessibility information for this book is coming soon. We're working to make it available as quickly as possible. Thank you for your patience.
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