D-Modules, Perverse Sheaves, and Representation Theory
Contributor(s): Hotta, Ryoshi [editor.] | Takeuchi, Kiyoshi [editor.] | Tanisaki, Toshiyuki [editor.] | SpringerLink (Online service).
Material type:
BookSeries: Progress in Mathematics: 236Publisher: Boston, MA : Birkhäuser Boston, 2008.Description: XI, 412 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817645236.Subject(s): Mathematics | Algebra | Algebraic geometry | Commutative algebra | Commutative rings | Group theory | Topological groups | Lie groups | Mathematics | Algebra | Group Theory and Generalizations | Topological Groups, Lie Groups | Commutative Rings and Algebras | Algebraic GeometryDDC classification: 512 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK10306 |
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.
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