{
  "id": "0712.0788",
  "version": "v3",
  "published": "2007-12-05T17:41:33.000Z",
  "updated": "2009-09-29T05:38:24.000Z",
  "title": "D-modules on the affine flag variety and representations of affine Kac-Moody algebras",
  "authors": [
    "Edward Frenkel",
    "Dennis Gaitsgory"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "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].",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-09-29T05:38:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R10",
      "17B67"
    ],
    "keywords": [
      "affine flag variety",
      "affine kac-moody algebras",
      "representations",
      "affine kac-moody lie algebra",
      "langlands dual group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0788F"
    }
  }
}