D-Modules, Perverse Sheaves, and Representation Theory

This work examines in detail the foundations of D-module theory and its intersection with perverse sheaves and representation theory. Systematic and carefully written, this is a unique and essential textbook at the graduate level for classroom use or self-study.

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.

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

Inhalt
D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic D-Modules.- RiemannHilbert Correspondence.- Perverse Sheaves.- Representation Theory.- Algebraic Groups and Lie Algebras.- Conjugacy Classes of Semisimple Lie Algebras.- Representations of Lie Algebras and D-Modules.- Character Formula of HighestWeight Modules.- Hecke Algebras and Hodge Modules.