{
  "id": "2408.09009",
  "version": "v1",
  "published": "2024-08-16T20:30:08.000Z",
  "updated": "2024-08-16T20:30:08.000Z",
  "title": "Reduced words for reflections in Weyl groups",
  "authors": [
    "Elizabeth Milićević"
  ],
  "comment": "17 pages; 7 tables and 1 figure best viewed in color",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The reflections in a Coxeter group are defined as conjugates of a single generator, and thus admit palindromic expressions as products of generators. Our main result gives closed formulas providing a palindromic reduced expression for each reflection in any finite Weyl group. There exist algorithmic methods for determining such reduced expressions, but explicit formulas have not been recorded outside of well-known special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-16T20:30:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reduced words",
      "reflection",
      "well-known special cases",
      "admit palindromic expressions",
      "finite weyl group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}