{
  "id": "0904.1820",
  "version": "v1",
  "published": "2009-04-11T19:13:27.000Z",
  "updated": "2009-04-11T19:13:27.000Z",
  "title": "Semisimple symplectic characters of finite unitary groups",
  "authors": [
    "C. Ryan Vinroot"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Let $G = {\\rm U}(2m, {\\mathbb F}_{q^2})$ be the finite unitary group, with $q$ the power of an odd prime $p$. We prove that the number of irreducible complex characters of $G$ with degree not divisible by $p$ and with Frobenius-Schur indicator -1 is $q^{m-1}$. We also obtain a combinatorial formula for the value of any character of ${\\rm U}(n, {\\mathbb F}_{q^2})$ at any central element, using the characteristic map of the finite unitary group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-11T19:13:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "05E05"
    ],
    "keywords": [
      "finite unitary group",
      "semisimple symplectic characters",
      "central element",
      "odd prime",
      "irreducible complex characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1820V"
    }
  }
}