{
  "id": "math/0501502",
  "version": "v1",
  "published": "2005-01-28T12:30:00.000Z",
  "updated": "2005-01-28T12:30:00.000Z",
  "title": "Lattices in finite real reflection groups",
  "authors": [
    "Thomas Brady",
    "Colum Watt"
  ],
  "comment": "29 pages, 3 figures",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "For a finite real reflection group $W$ with Coxeter element $\\gamma$ we give a uniform proof that the closed interval, $[I, \\gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the construction of a simplicial complex which can be embedded in the type W simplicial generalised associahedron.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-28T12:30:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "finite real reflection group",
      "simplicial generalised associahedron",
      "uniform proof",
      "partial order",
      "reflection length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1502B"
    }
  }
}