D-Modules, Perverse Sheaves, and Representation Theory (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
412
Utgivningsdatum
2007-11-01
Upplaga
English
Förlag
Birkhauser Boston Inc
Översättare
Kiyoshi Takeuchi
Medarbetare
Takeuchi, Kiyoshi
Illustratör/Fotograf
20 schw-w Zeichn
Illustrationer
XI, 412 p.
Dimensioner
234 x 156 x 24 mm
Vikt
772 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9780817643638
D-Modules, Perverse Sheaves, and Representation Theory (inbunden)

D-Modules, Perverse Sheaves, and Representation Theory

Inbunden Engelska, 2007-11-01
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D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, 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. 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, representation theory.
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Recensioner i media

From the reviews: "A self-contained introduction to D-modules, with the aim of showing how they were used to solve the Kazhdan-Lusztig conjecture. ... present book can be used as a good reference on D-modules and on advanced representation theory of semisimple Lie algebras, but especially as a detailed account on the relations between them; in fact, in our opinion this is the first and very welcome complete work devoted to a mainstream research field (the 'Algebraic Analysis' approach to representation theory) which remains very active almost thirty years." (Corrado Marastoni, Mathematical Reviews, Issue 2008 k) "The present book provides a reader-friendly treatment of the subject, suitable for graduate students who wish to enter the area. Part I of the book presents the theory of D-modules ... . The treatment in the book is quite complete ... . Part II provides the necessary background in the structure of semi-simple Lie algebras and their representations." (Dennis Gaitsgory, Bulletin of the American Mathematical Society, Vol. 47 (4), October, 2010)

Innehållsförteckning

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.