D-Modules, Perverse Sheaves, and Representation Theory (Progress in Mathematics, 236)

Description

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. Review: Excelente libro - Excelente libro Review: Fabulous - This book, on a pretty austere but exceedingly important subject (particulalry given the power and impact of the Riemann-Hilbert Correspondence) is a wonderful resource --- in fact, the book gives a full proof of "Riemann-Hilbert"!Additionally, the authors discuss a beautiful and deep connection to representation theory, which is not present in other texts. This makes the book particularly useful to people seeking to apply this material to other areas. Finally, the book is very well written and accessible, provided of course that the reader has the required background (Recommendation: first study Kashiwara-Shapira's "Sheaves on Manifolds.").