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- Title
D-modules on the affine flag variety and representations of affine Kac-Moody algebras.
- Authors
Edward Frenkel; Dennis Gaitsgory
- Abstract
The present paper studies the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme $G((t))/I$, where $I$ is the Iwahori subgroup. We prove a localization-type result, which establishes an equivalence between certain subcategories on both sides. We also establish an equivalence between a certain subcategory of Kac-Moody modules, and the category of quasi-coherent sheaves on the scheme of Miura opers for the Langlands dual group, thereby proving a conjecture of the authors in 2006.
- Subjects
D-modules; AFFINE algebraic groups; REPRESENTATIONS of algebras; KAC-Moody algebras; CATEGORIES (Mathematics); LOCALIZATION theory
- Publication
Representation Theory, 2009, Vol 13, Issue 22, p470
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/S1088-4165-09-00360-4