D-Modules, Perverse Sheaves, and Representation Theory, Vol. 236

✍ Scribed by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki, Kiyoshi Takeuchi

• Publisher: Birkhäuser Boston
• Year: 2007
• Tongue: English
• Leaves: 407
• Series: Progress in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface......Page 5
Contents......Page 7
Relation Among Chapters......Page 11
Introduction......Page 12
Part I: D-Modules and Perverse Sheaves......Page 23
Preliminary Notions......Page 24
Coherent D-Modules......Page 66
Holonomic D-Modules......Page 90
Analytic D-Modules and the de Rham Functor......Page 107
Theory of Meromorphic Connections......Page 135
Regular Holonomic D-Modules......Page 168
Riemann–Hilbert Correspondence......Page 178
Perverse Sheaves......Page 187
Part II: Representation Theory......Page 232
Algebraic Groups and Lie Algebras......Page 233
Conjugacy Classes of Semisimple Lie Algebras......Page 262
Representations of Lie Algebras and D-Modules......Page 274
Character Formula of HighestWeight Modules......Page 291
Hecke Algebras and Hodge Modules......Page 306
Algebraic Varieties......Page 322
Derived Categories and Derived Functors......Page 331
Sheaves and Functors in Derived Categories......Page 350
Filtered Rings......Page 364
Symplectic Geometry......Page 377
References......Page 384
List of Notation......Page 394
Index......Page 399