{
  "id": "math/0303173",
  "version": "v3",
  "published": "2003-03-13T19:50:11.000Z",
  "updated": "2004-01-15T19:22:04.000Z",
  "title": "D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras",
  "authors": [
    "E. Frenkel",
    "D. Gaitsgory"
  ],
  "comment": "Revised version; to appear in Duke Math. Journal",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let ${\\mathfrak g}$ be a simple Lie algebra. For a level $\\kappa$ (thought of as a symmetric ${\\mathfrak g}$-invariant form of ${\\mathfrak g}$), let $\\hat{\\mathfrak g}_\\kappa$ be the corresponding affine Kac-Moody algebra. Let $Gr_G$ be the affine Grassmannian of ${\\mathfrak g}$, and let $D_\\kappa(Gr_G)-mod$ be the category of $\\kappa$-twisted right D-modules on $Gr_G$. By taking global sections of a D-module, we obtain a functor $\\Gamma:D_\\kappa(Gr_G)-mod\\to {\\mathfrak g}_\\kappa-mod$. It is known that this functor is exact and faithful when $\\kappa$ is negative or irrational. In this paper, we show that the functor $\\Gamma$ is exact and faithful also when $\\kappa$ is the critical level.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-01-15T19:22:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine grassmannian",
      "representations",
      "simple lie algebra",
      "corresponding affine kac-moody algebra",
      "invariant form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3173F"
    }
  }
}