D-modules on the affine flag variety and representations of affine Kac-Moody algebras

Details D-modules on the affine flag variety and representations of affine Kac-Moody algebras D-modules on the affine flag variety and representations of affine Kac-Moody algebras

2007-12-05

arxiv.org/abs/0712.0788v3

Mathematics

Representation Theory

Scientific paper

We study 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 [FG2].

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