{
  "id": "1011.5791",
  "version": "v2",
  "published": "2010-11-26T14:05:43.000Z",
  "updated": "2011-04-01T16:21:35.000Z",
  "title": "On sheets of conjugacy classes in good characteristic",
  "authors": [
    "Giovanna Carnovale",
    "Francesco Esposito"
  ],
  "comment": "After acceptance and typesetting of the journal version of the paper, we discovered that the notions of Levi envelope, Jordan class and exceptional element in an algebraic group had already appeared in G. Lusztig's paper \"Intersection cohomology complexes on a reductive group\", Invent. Math. 75 no. 2, 205-272 (1984); online final version published online in International Mathematics Research Notices 2011",
  "doi": "10.1093/imrn/rnr047",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We show that the sheets for a connected reductive algebraic group G over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with G-conjugacy classes of triples (M, Z(M)^\\circ t, O) where M is the connected centralizer of a semisimple element in G, Z(M)^\\circ t is a suitable coset in Z(M)/Z(M)^\\circ and O is a rigid unipotent conjugacy class in M. Any semisimple element is contained in a unique sheet S and S corresponds to a triple with O={1}. The sheets in G containing a unipotent conjugacy class are precisely those corresponding to triples for which M is a Levi subgroup of a parabolic subgroup of G and such a class is unique.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-01T16:21:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G15",
      "14L30"
    ],
    "keywords": [
      "characteristic",
      "semisimple element",
      "rigid unipotent conjugacy class",
      "connected reductive algebraic group",
      "levi subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5791C"
    }
  }
}