{
  "id": "0906.1790",
  "version": "v2",
  "published": "2009-06-09T17:37:00.000Z",
  "updated": "2009-06-10T14:53:46.000Z",
  "title": "Counting p'-characters in finite reductive groups",
  "authors": [
    "Olivier Brunat"
  ],
  "doi": "10.1112/jlms/jdq001",
  "categories": [
    "math.RT"
  ],
  "abstract": "This article is concerned with the relative McKay conjecture for finite reductive groups. Let G be a connected reductive group defined over the finite field F_q of characteristic p>0 with corresponding Frobenius map F. We prove that if the F-coinvariants of the component group of the center of G has prime order and if p is a good prime for G, then the relative McKay conjecture holds for G at the prime p. In particular, this conjecture is true for G^F in defining characteristic for G a simple and simply-connected group of type B_n, C_n, E_6 and E_7. Our main tools are the theory of Gelfand-Graev characters for connected reductive groups with disconnected center developed by Digne-Lehrer-Michel and the theory of cuspidal Levi subgroups. We also explicitly compute the number of semisimple classes of G^F for any simple algebraic group G.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-10T14:53:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C33"
    ],
    "keywords": [
      "finite reductive groups",
      "connected reductive group",
      "simple algebraic group",
      "cuspidal levi subgroups",
      "relative mckay conjecture holds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1790B"
    }
  }
}