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Viser: D-Modules, Perverse Sheaves, and Representation Theory
D-Modules, Perverse Sheaves, and Representation Theory
Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki og Kiyoshi Takeuchi
(2007)
Sprog: Engelsk
Birkhäuser Boston
1.163,00 kr.
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Detaljer om varen
- 1. Udgave
- Hardback: 412 sider
- Udgiver: Birkhäuser Boston (November 2007)
- Forfattere: Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki og Kiyoshi Takeuchi
- ISBN: 9780817643638
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, 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 Kazhdan-Lusztig polynomials 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, representation theory.
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.
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