{
  "id": "1001.4283",
  "version": "v1",
  "published": "2010-01-24T23:16:24.000Z",
  "updated": "2010-01-24T23:16:24.000Z",
  "title": "Pieces of nilpotent cones for classical groups",
  "authors": [
    "Pramod N. Achar",
    "Anthony Henderson",
    "Eric Sommers"
  ],
  "comment": "32 pages",
  "journal": "Representation Theory 15 (2011), 584-616",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and Kato's exotic nilpotent cone. We prove that the number of $\\F_q$-points in each nilpotent orbit of type $B_n$ or $C_n$ equals that in a corresponding union of orbits, called a type-$B$ or type-$C$ piece, in the exotic nilpotent cone. This is a finer version of Lusztig's result that corresponding special pieces in types $B_n$ and $C_n$ have the same number of $\\F_q$-points. The proof requires studying the case of characteristic 2, where more direct connections between the three nilpotent cones can be established. We also prove that the type-$B$ and type-$C$ pieces of the exotic nilpotent cone are smooth in any characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-24T23:16:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B08",
      "20G15",
      "14L30"
    ],
    "keywords": [
      "classical groups",
      "katos exotic nilpotent cone",
      "nilpotent orbit",
      "compare orbits",
      "finer version"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.4283A"
    }
  }
}