{
  "id": "1207.5557",
  "version": "v1",
  "published": "2012-07-23T23:05:17.000Z",
  "updated": "2012-07-23T23:05:17.000Z",
  "title": "An inverse Satake isomorphism in characteristic p",
  "authors": [
    "Rachel Ollivier"
  ],
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let F be a local field with finite residue field of characteristic p and k an algebraic closure of the residue field. Let G be the group of F-points of a F-split connected reductive group. In the apartment corresponding to a chosen maximal split torus of T, we fix a hyperspecial vertex and denote by K the corresponding maximal compact subgroup of G. Given an irreducible smooth k-representation $\\rho$ of K, we construct an isomorphism from the affine semigroup k-algebra of the dominant cocharacters of T onto the Hecke algebra $H(G, \\rho)$. In the case when the derived subgroup of G is simply connected, we prove furthermore that our isomorphism is the inverse to the Satake isomorphism constructed by Herzig.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-23T23:05:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22E50"
    ],
    "keywords": [
      "inverse satake isomorphism",
      "characteristic",
      "chosen maximal split torus",
      "finite residue field",
      "affine semigroup k-algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5557O"
    }
  }
}