{
  "id": "math/0211067",
  "version": "v3",
  "published": "2002-11-04T18:54:52.000Z",
  "updated": "2003-10-22T19:12:10.000Z",
  "title": "On automorphic sheaves on Bun_G",
  "authors": [
    "Sergey Lysenko"
  ],
  "comment": "30 pages, updated version",
  "categories": [
    "math.RT",
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let X be a smooth projective connected curve over an algebraically closed field k of positive characteristic. Let G be a reductive group over k, \\gamma be a dominant coweight for G, and E be an \\ell-adic \\check{G}-local system on X, where \\check{G} denotes the Langlands dual group. Let \\Bun_G be the moduli stack of G-bundles on X. Under some conditions on the triple (G,\\gamma,E) we propose a conjectural construction of a distinguished E-Hecke automorphic sheaf on \\Bun_G. We are motivated by a construction of automorphic forms suggested by Ginzburg, Rallis and Soudry in [6,7]. We also generalize Laumon's theorem ([10], Theorem 4.1) for our setting. Finally, we formulate an analog of the Vanishing Conjecture of Frenkel, Gaitsgory and Vilonen for Levi subgroups of G.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-10-22T19:12:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R39",
      "14H60"
    ],
    "keywords": [
      "automorphic sheaves",
      "langlands dual group",
      "distinguished e-hecke automorphic sheaf",
      "levi subgroups",
      "moduli stack"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11067L"
    }
  }
}