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＜電子ブック＞
D-Modules, Perverse Sheaves, and Representation Theory / by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
(Progress in Mathematics. ISSN:2296505X ; 236)

版	1st ed. 2008.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2008
本文言語	英語
大きさ	XI, 412 p : online resource
著者標目	*Hotta, Ryoshi author Takeuchi, Kiyoshi author Tanisaki, Toshiyuki author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Group theory LCSH:Topological groups LCSH:Lie groups LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry FREE:Algebra FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups FREE:Commutative Rings and Algebras FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4523-6

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