{
  "id": "1412.5428",
  "version": "v1",
  "published": "2014-12-17T15:09:52.000Z",
  "updated": "2014-12-17T15:09:52.000Z",
  "title": "Coxeter groups and automorphisms",
  "authors": [
    "Meinolf Geck",
    "Lacrimioara Iancu"
  ],
  "comment": "4 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(W,S)$ be a Coxeter system and $\\Gamma$ be a group of automorphisms of $W$ such that $\\gamma(S)=S$ for all $\\gamma \\in \\Gamma$. Then it is known that the group of fixed points $W^\\Gamma$ is again a Coxeter group with a canonically defined set of generators. The usual proofs of this fact rely on the reflection representation of $W$. Here, we give a proof which only uses the combinatorics of reduced expressions in $W$. As a by-product, this shows that the length function on $W$ restricts to a weight function on $W^\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-17T15:09:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coxeter group",
      "automorphisms",
      "weight function",
      "length function",
      "coxeter system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5428G"
    }
  }
}