{
  "id": "1506.07690",
  "version": "v1",
  "published": "2015-06-25T10:19:54.000Z",
  "updated": "2015-06-25T10:19:54.000Z",
  "title": "Characters of odd degree",
  "authors": [
    "Gunter Malle",
    "Britta Späth"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes $\\ell$ such that a Sylow $\\ell$-subgroup or its maximal normal abelian subgroup is contained in a maximally split torus by means of a new equivariant version of Harish-Chandra induction. Specifics of characters of odd degree, namely that they only lie in very particular Harish-Chandra series then allow us to deduce from it the McKay conjecture for the prime~$2$, hence for characters of odd degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T10:19:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C33",
      "20C08"
    ],
    "keywords": [
      "odd degree",
      "characters",
      "mckay conjecture",
      "maximal normal abelian subgroup",
      "harish-chandra induction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607690M"
    }
  }
}