D-Modules on the Affine Flag Variety and Representations of Affine Kac-Moody Algebras

 Title: D-Modules on the Affine Flag Variety and Representations of Affine Kac-Moody Algebras Author: Frenkel, Edward; Gaitsgory, Dennis Note: Order does not necessarily reflect citation order of authors. Citation: Frenkel, Edward, and Dennis Gaitsgory. 2009. D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Representation Theory 13: 470-608. Full Text & Related Files: 0712.0788v3.pdf (1.030Mb; PDF) 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. Published Version: doi:10.1090/S1088-4165-09-00360-4 Other Sources: http://arxiv.org/abs/0712.0788 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10043338 Downloads of this work: