{
  "id": "1712.09263",
  "version": "v1",
  "published": "2017-12-26T13:11:54.000Z",
  "updated": "2017-12-26T13:11:54.000Z",
  "title": "The irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(p^f)$ and $\\mathrm{E}_6(p^f)$",
  "authors": [
    "Tung Le",
    "Kay Magaard",
    "Alessandro Paolini"
  ],
  "comment": "32 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(q)$ and $\\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization is uniform for $p \\ge 3$ in type $\\mathrm{D}_6$ and for $p \\ge 5$ in type $\\mathrm{E}_6$, while the prime $2$ in type $\\mathrm{D}_6$ and the primes $2,$ $3$ in type $\\mathrm{E}_6$ yield character degrees of the form $q^m/p^i$ which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters of a classical group of degree $q^m/p^i$ where $i > 1$ which occurs in type $\\mathrm{D}_6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-26T13:11:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20C15"
    ],
    "keywords": [
      "irreducible characters",
      "chevalley groups",
      "yield character degrees",
      "arbitrary power",
      "generic situations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}