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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.