{
  "id": "2002.05468",
  "version": "v1",
  "published": "2020-02-13T12:16:05.000Z",
  "updated": "2020-02-13T12:16:05.000Z",
  "title": "Braid groups of normalizers of reflection subgroups",
  "authors": [
    "Thomas Gobet",
    "Anthony Henderson",
    "Ivan Marin"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-13T12:16:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reflection subgroup",
      "normalizer",
      "hecke algebra",
      "finite complex reflection group",
      "standard basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}