D-Modules, Perverse Sheaves, and Representation Theory

Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki (auth.), Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki (eds.)081764363X, 9780817643638

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 :
Front Matter….Pages I-11
Front Matter….Pages 13-13
Preliminary Notions….Pages 15-56
Coherent D-Modules….Pages 57-80
Holonomic D-Modules….Pages 81-97
Analytic D-Modules and the de Rham Functor….Pages 99-126
Theory of Meromorphic Connections….Pages 127-159
Regular Holonomic D-Modules….Pages 161-170
Riemann–Hilbert Correspondence….Pages 171-179
Perverse Sheaves….Pages 181-225
Front Matter….Pages 227-227
Algebraic Groups and Lie Algebras….Pages 229-257
Conjugacy Classes of Semisimple Lie Algebras….Pages 259-270
Representations of Lie Algebras and D-Modules….Pages 271-287
Character Formula of HighestWeight Modules….Pages 289-303
Hecke Algebras and Hodge Modules….Pages 305-320
Back Matter….Pages 321-407