TY  - BOOK
AU  - Hotta,Ryoshi
AU  - Takeuchi,Kiyoshi
AU  - Tanisaki,Toshiyuki
ED  - SpringerLink (Online service)
TI  - D-Modules, Perverse Sheaves, and Representation Theory
T2  - Progress in Mathematics
SN  - 9780817645236
U1  - 512 23
PY  - 2008///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - ALGEBRA
KW  - GEOMETRY, ALGEBRAIC
KW  - GROUP THEORY
KW  - TOPOLOGICAL GROUPS
KW  - GROUP THEORY AND GENERALIZATIONS
KW  - TOPOLOGICAL GROUPS, LIE GROUPS
KW  - COMMUTATIVE RINGS AND ALGEBRAS
KW  - ALGEBRAIC GEOMETRY
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-0-8176-4523-6
ER  -