D Modules, Perverse Sheaves, and Representation Theory

D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. 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. This work examines in detail the foundations of D-module theory and its intersection with cohomology groups and representation theory. This systematic and carefully written exposition begins with preliminary concepts before focusing on some basic but important theories that have emerged in the last few decades. Significant topics that have emerged as studies in their own right include a treatment of the theory of holonomic D-modules, perverse sheaves, the Riemann-Hilbert correspondence, Hodge modules, and Kazhdan-Lusztig polynomials. To further aid the reader, appendices are provided as reviews for the theory of derived categories and algebraic varieties."D-modules, Perverse Sheaves, and Representation Theory" is a unique and essential textbook at the graduate level for classroom use or self-study. Graduate students and researchers in algebra and representation theory will benefit greatly from this work.