By: Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki

Hardcover

Click on the Google Preview image above to read some pages of 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.

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)

D-Modules and Perverse Sheaves
Preliminary Notions	p. 15
Coherent D-Modules	p. 57
Holonomic D-Modules	p. 81
Analytic D-Modules and the de Rham Functor	p. 99
Theory of Meromorphic Connections	p. 127
Regular Holonomic D-Modules	p. 161
Riemann-Hilbert Correspondence	p. 171
Perverse Sheaves	p. 181
Representation Theory
Algebraic Groups and Lie Algebras	p. 229
Conjugacy Classes of Semisimple Lie Algebras	p. 259
Representations of Lie Algebras and D-Modules	p. 271
Character Formula of Highest Weight Modules	p. 289
Hecke Algebras and Hodge Modules	p. 305
Algebraic Varieties	p. 321
Derived Categories and Derived Functors	p. 331
Sheaves and Functors in Derived Categories	p. 351
Filtered Rings	p. 365
Symplectic Geometry	p. 379
References	p. 387
List of Notation	p. 397
Index	p. 403
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780817643638
ISBN-10: 081764363X
Series: Progress in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 426
Published: 7th November 2007
Publisher: SPRINGER VERLAG GMBH
Dimensions (cm): 23.393 x 15.596  x 2.388
Weight (kg): 0.771