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

@inproceedings{Frenkel2009DModulesOT,
  title={D-Modules on the Affine Flag Variety and Representations of Affine Kac-Moody Algebras},
  author={Edward Frenkel and DENNIS GAITSGORY},
  year={2009}
}
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… CONTINUE READING