{
  "id": "math/0201073",
  "version": "v6",
  "published": "2002-01-09T18:11:33.000Z",
  "updated": "2020-02-11T20:29:16.000Z",
  "title": "Perverse sheaves on affine flags and Langlands dual group",
  "authors": [
    "Sergey Arkhipov",
    "Roman Bezrukavnikov"
  ],
  "comment": "32 pages; some corrections, epigraph added. See arXiv:1807.07614 for corrected proof of Lemma 5",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "The geometric Satake isomorphism is an equivalence between the categories of spherical perverse sheaves on affine Grassmanian and the category of representations of the Langlands dual group. We provide a similar description for derived categories of l-adic sheaves on an affine flag variety which are geometric counterparts of a maximal commutative subalgebra in the Iwahori Hecke algebra; of the anti-spherical module over this algebra; and of the space of Iwahori-invariant Whitakker functions.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-09-06T00:18:47.000Z",
      "comment": "32 pages; some corrections, epigraph added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v6",
      "updated": "2020-02-11T20:29:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langlands dual group",
      "iwahori-invariant whitakker functions",
      "affine flag variety",
      "iwahori hecke algebra",
      "geometric satake isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1073A"
    }
  }
}