Hotta / Takeuchi / Tanisaki D-Modules, Perverse Sheaves, and Representation Theory
1. Auflage 2007
ISBN: 978-0-8176-4523-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 407 Seiten, Web PDF
Reihe: Mathematics and Statistics
ISBN: 978-0-8176-4523-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory.
Key to is the authors' essential algebraic-analytic approach to the theory, which connects -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 -modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using -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.
Zielgruppe
Research
Weitere Infos & Material
D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic D-Modules.- Riemann–Hilbert Correspondence.- Perverse Sheaves.- Representation Theory.- Algebraic Groups and Lie Algebras.- Conjugacy Classes of Semisimple Lie Algebras.- Representations of Lie Algebras and D-Modules.- Character Formula of HighestWeight Modules.- Hecke Algebras and Hodge Modules.
