{
  "id": "1211.5366",
  "version": "v2",
  "published": "2012-11-22T20:28:40.000Z",
  "updated": "2014-08-15T18:55:20.000Z",
  "title": "Compatibility between Satake and Bernstein-type isomorphisms in characteristic p",
  "authors": [
    "Rachel Ollivier"
  ],
  "comment": "The new version contains the classification of the simple supersingular Hecke modules in the case of a general split group",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We study the center of the pro-p Iwahori-Hecke ring H of a connected split p-adic reductive group G. For k an algebraically closed field with characteristic p, we prove that the center of the k-algebra H_k:= H\\otimes_Z k contains an affine semigroup algebra which is naturally isomorphic to the Hecke algebra attached to any irreducible smooth k-representation of a given hyperspecial maximal compact subgroup of G. This isomorphism is obtained using the inverse Satake isomorphism constructed in arXiv:1207.5557. We apply this to classify the simple supersingular H_k-modules, study the supersingular block in the category of finite length H_k-modules, and relate the latter to supersingular representations of G.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-15T18:55:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22E50"
    ],
    "keywords": [
      "bernstein-type isomorphisms",
      "characteristic",
      "hyperspecial maximal compact subgroup",
      "compatibility",
      "supersingular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5366O"
    }
  }
}