{
  "id": "1512.02678",
  "version": "v1",
  "published": "2015-12-08T22:09:51.000Z",
  "updated": "2015-12-08T22:09:51.000Z",
  "title": "Constructing characters of Sylow $p$-subgroups of finite Chevalley groups",
  "authors": [
    "Simon M. Goodwin",
    "Tung Le",
    "Kay Magaard",
    "Alessandro Paolini"
  ],
  "comment": "37 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Let $q$ be a power of a prime $p$, let $G$ be a finite Chevalley group over $\\mathbb{F}_q$ and let $U$ be a Sylow $p$-subgroup of $G$; we assume that $p$ is not a very bad prime for $G$. We explain a procedure of reduction of irreducible complex characters of $U$, which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of $U$ along with a means to construct these characters as induced characters. A focus in this paper is determining the parametrization when $G$ is of type $\\mathrm{F}_4$, where we observe that the parametrization is \"uniform\" over good primes $p > 3$, but differs for the bad prime $p = 3$. We also explain how it has been applied for all groups of rank $4$ or less.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-08T22:09:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite chevalley group",
      "constructing characters",
      "bad prime",
      "parametrization",
      "irreducible complex characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}