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Birkhäuser - Birkhäuser Mathematics | D-Modules, Perverse Sheaves, and Representation Theory

D-Modules, Perverse Sheaves, and Representation Theory

Series: Progress in Mathematics, Vol. 236

Hotta, Ryoshi, Takeuchi, Kiyoshi, Tanisaki, Toshiyuki

Translated by Takeuchi, K.

2008, XI, 412 p.

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  • The unique text treating an algebraic-analytic approach to D-module theory
  • Examines D-module theory, connecting algebraic geometry and representation theory
  • Detailed examination with excellent proof of the Riemann-Hilbert correspondence

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.

Content Level » Research

Keywords » D-Modules - Hecke algebras - Hodge modules - Meromorphic function - Representation theory - algebra - algebraic varieties - perverse sheaves

Related subjects » Birkhäuser Mathematics

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