Wall-crossing functors and 𝒟-modules
Authors:
- Alexander BeilinsonABAlexander Beilinson
- Victor GinzburgVGVictor Ginzburg
- 11 January 1999
- journal article
- Published by American Mathematical Society (AMS) in Representation Theory
- Vol. 3 (1) , 1-31
Abstract
We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D {\mathcal {D}} -modules. This functorial machinery is then used to prove the Endomorphism-theorem and the Structure-theorem; two important results were established earlier by W. Soergel in a totally different way. Other applications to the category O {\mathcal {O}} of Bernstein-Gelfand-Gelfand are given, and some conjectural relationships between Koszul duality, Verdier duality and convolution functors are discussed. A geometric interpretation of tilting modules is given.Keywords
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This publication has 13 references indexed in Scilit:
- Charakterformeln für Kipp-Moduln über Kac-Moody-AlgebrenRepresentation Theory, 1997
- Koszul Duality Patterns in Representation TheoryJournal of the American Mathematical Society, 1996
- Kazhdan-Lusztig conjecture for affine Lie algebras with negative levelDuke Mathematical Journal, 1995
- Equivariant Sheaves and Functors1994
- The combinatorics of Harish-Chandra bimodules.Journal für die reine und angewandte Mathematik (Crelles Journal), 1992
- Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur WeylgruppeJournal of the American Mathematical Society, 1990
- G-modules, Springer's representations and bivariant Chern classesAdvances in Mathematics, 1986
- Moduln mit einem höchsten Gewicht1979
- Tensor Products of Finite and Infinite Dimensional Representations of Semisimple Lie GroupsAnnals of Mathematics, 1977
- On the tensor product of a finite and an infinite dimensional representationJournal of Functional Analysis, 1975