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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.

Linear algebraic groups. --- D-modules. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Modules (Algebra) --- Algebraic groups, Linear --- Geometry, Algebraic --- Algebraic varieties --- Algebra. --- Group theory. --- Topological Groups. --- Geometry, algebraic. --- Group Theory and Generalizations. --- Topological Groups, Lie Groups. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Groups, Topological --- Continuous groups --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- Mathematical analysis --- Topological groups. --- Lie groups. --- Commutative algebra. --- Commutative rings. --- Algebraic geometry. --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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Group theory --- Ordered algebraic structures --- Algebra --- Topological groups. Lie groups --- Geometry --- algebra --- landmeetkunde --- topologie (wiskunde) --- wiskunde