{
  "id": "math/0611323",
  "version": "v2",
  "published": "2006-11-10T21:30:58.000Z",
  "updated": "2007-08-07T13:16:53.000Z",
  "title": "Spherical varieties and Langlands duality",
  "authors": [
    "D. Gaitsgory",
    "D. Nadler"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space of X. In this paper, we associate to X a connected reductive complex algebraic subgroup $\\check H$ of the dual group $\\check G$. The construction of $\\check H$ is via Tannakian formalism: we identify a certain tensor category Q(Z) of perverse sheaves on Z with the category of finite-dimensional representations of $\\check H$. Combinatorial shadows of the group $\\check H$ govern many aspects of the geometry of X such as its compactifications and invariant differential operators. When X is a symmetric variety, the group $\\check H$ coincides with that associated to the corresponding real form of G via the (real) geometric Satake correspondence.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-07T13:16:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langlands duality",
      "spherical varieties",
      "invariant differential operators",
      "connected reductive complex algebraic subgroup",
      "connected reductive complex algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11323G"
    }
  }
}