{
  "id": "0711.2959",
  "version": "v2",
  "published": "2007-11-19T15:47:20.000Z",
  "updated": "2008-07-11T14:17:13.000Z",
  "title": "On conjugacy of unipotent elements in finite groups of Lie type",
  "authors": [
    "Simon M. Goodwin",
    "Gerhard Roehrle"
  ],
  "comment": "9 pages, Minor changes and corrections",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let $\\bfG$ be a connected reductive algebraic group defined over $\\F_q$, where $q$ is a power of a prime $p$ that is good for $\\bfG$. Let $F$ be the Frobenius morphism associated with the $\\FF_q$-structure on $\\bfG$ and set $G = \\bfG^F$, the fixed point subgroup of $F$. Let $\\bfP$ be an $F$-stable parabolic subgroup of $\\bfG$ and let $\\bfU$ be the unipotent radical of $\\bfP$; set $P = \\bfP^F$ and $U = \\bfU^F$. Let $G_\\uni$ be the set of unipotent elements in $G$. In this note we show that the number of conjugacy classes of $U$ in $G_\\uni$ is given by a polynomial in $q$ with integer coefficients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-11T14:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40",
      "20E45",
      "20D20"
    ],
    "keywords": [
      "unipotent elements",
      "finite groups",
      "lie type",
      "reductive algebraic group",
      "fixed point subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2959G"
    }
  }
}