{
  "id": "2105.08104",
  "version": "v1",
  "published": "2021-05-17T18:31:33.000Z",
  "updated": "2021-05-17T18:31:33.000Z",
  "title": "The Hurwitz action in complex reflection groups",
  "authors": [
    "Joel Brewster Lewis",
    "Jiayuan Wang"
  ],
  "comment": "30 pages plus a Sage code file",
  "journal": "Combinatorial Theory, 2(1), #12, 2022",
  "doi": "10.5070/C62156884",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive and give a simple criterion to tell when two shortest reflection factorizations belong to the same Hurwitz orbit. We also characterize the quasi-Coxeter elements (those with a shortest reflection factorization that generates the whole group) in $G(m, p, n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-17T18:31:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex reflection groups",
      "hurwitz action",
      "shortest reflection factorizations belong",
      "enumerate hurwitz orbits",
      "simple criterion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}