{
  "id": "2401.06516",
  "version": "v1",
  "published": "2024-01-12T11:30:57.000Z",
  "updated": "2024-01-12T11:30:57.000Z",
  "title": "Hook formula for Coxeter groups via the twisted group ring",
  "authors": [
    "Leonardo C. Mihalcea",
    "Hiroshi Naruse",
    "Changjian Su"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.CO",
    "math.GR",
    "math.RA"
  ],
  "abstract": "We use Kostant and Kumar's twisted group ring and its dual to formulate and prove a generalization of Nakada's colored hook formula for any Coxeter groups. For dominant minuscule elements of the Weyl group of a Kac--Moody algebra, this provides another short proof of Nakada's colored hook formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-12T11:30:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "05E16",
      "16S35"
    ],
    "keywords": [
      "coxeter groups",
      "nakadas colored hook formula",
      "dominant minuscule elements",
      "weyl group",
      "kac-moody algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}