Frenkel, EdwardGaitsgory, Dennis2012-12-122009Frenkel, Edward, and Dennis Gaitsgory. 2009. D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Representation Theory 13: 470-608.1088-4165http://nrs.harvard.edu/urn-3:HUL.InstRepos:10043338The 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.en-USalgebraic geometryrepresentation theoryJournal Article2012-12-1210.1090/S1088-4165-09-00360-4