{
  "id": "0910.0923",
  "version": "v3",
  "published": "2009-10-06T05:05:38.000Z",
  "updated": "2015-06-04T18:11:45.000Z",
  "title": "Non-cancellable elements in type affine $C$ Coxeter groups",
  "authors": [
    "Dana C. Ernst"
  ],
  "comment": "Updated contact information and made a few cosmetic improvements. 21 pages, 22 figures",
  "journal": "Int. Electron. J. Algebra, 8:191-218, 2010",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Let $(W,S)$ be a Coxeter system and suppose that $w \\in W$ is fully commutative (in the sense of Stembridge) and has a reduced expression beginning (respectively, ending) with $s \\in S$. If there exists $t\\in S$ such that $s$ and $t$ do not commute and $tw$ (respectively, $wt$) is no longer fully commutative, we say that $w$ is left (respectively, right) weak star reducible by $s$ with respect to $t$. In this paper, we classify the fully commutative elements in Coxeter groups of types $B$ and affine $C$ that are irreducible under weak star reductions. In a sequel to this paper, the classification of the weak star irreducible elements in a Coxeter system of type affine $C$ will provide the groundwork for inductive arguments used to prove the faithfulness of a generalized Temperley--Lieb algebra of type affine $C$ by a particular diagram algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-28T19:27:12.000Z",
      "comment": "Revised in light of referee's comments. To appear in International Electronic Journal of Algebra. 21 pages, 22 figures",
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-06-04T18:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "06A07",
      "20C08"
    ],
    "keywords": [
      "type affine",
      "coxeter groups",
      "non-cancellable elements",
      "coxeter system",
      "weak star irreducible elements"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0923E"
    }
  }
}