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Geometric quantization. --- D-modules. --- Noncommutative differential geometry. --- Poisson manifolds. --- Quantification géométrique. --- D-modules, Théorie des. --- Géométrie différentielle non commutative. --- Poisson, Variétés de.

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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.

Ordered algebraic structures --- Geometry --- algebra --- topologie (wiskunde) --- Topological groups. Lie groups --- Algebra --- landmeetkunde --- wiskunde --- Group theory --- Représentations d'algèbres de Lie --- Representations of Lie algebras --- Linear algebraic groups. --- D-modules. --- Representations of groups. --- Groupes algébriques linéaires --- D-modules, Théorie des --- Représentations de groupes