D-Modules, Perverse Sheaves, and Representation Theory

• Corporate Author: SpringerLink (Online service)
• Other Authors: Hotta, Ryoshi (Editor), Takeuchi, Kiyoshi (Editor), Tanisaki, Toshiyuki (Editor)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2008.
• Series: Progress in Mathematics ; 236
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Group theory.; Topological groups.; Lie groups.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Commutative Rings and Algebras.; Algebraic Geometry.

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,...

Table of Contents:

• 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
• Riemann–Hilbert 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.