{
  "id": "2309.15586",
  "version": "v1",
  "published": "2023-09-27T11:41:52.000Z",
  "updated": "2023-09-27T11:41:52.000Z",
  "title": "Orthogonal irreducible representations of finite solvable groups in odd dimension",
  "authors": [
    "Mikko Korhonen"
  ],
  "comment": "to appear in Bull. Lond. Math. Soc",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "We prove that if $G$ is a finite irreducible solvable subgroup of an orthogonal group $O(V,Q)$ with $\\dim V$ odd, then $G$ preserves an orthogonal decomposition of $V$ into $1$-spaces. In particular $G$ is monomial. This generalizes a theorem of Rod Gow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-27T11:41:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20H20",
      "20C99"
    ],
    "keywords": [
      "finite solvable groups",
      "orthogonal irreducible representations",
      "odd dimension",
      "finite irreducible solvable subgroup",
      "orthogonal group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}