{
  "id": "1807.08605",
  "version": "v1",
  "published": "2018-07-23T13:39:10.000Z",
  "updated": "2018-07-23T13:39:10.000Z",
  "title": "Shadows in Coxeter groups",
  "authors": [
    "Marius Graeber",
    "Petra Schwer"
  ],
  "comment": "30 pages, 8 figures",
  "categories": [
    "math.CO",
    "math.GR",
    "math.RT"
  ],
  "abstract": "For a given $w$ in a Coxeter group $W$ the elements $u$ smaller than $w$ in Bruhat order are the end-alcoves of stammering galleries of type $w$ in the Coxeter complex. We generalize this notion and consider sets of end-alcoves of galleries that are positively folded with respect to certain orientation $\\phi$ of $\\Sigma$. We call these sets \\emph{shadows}. In this paper we will introduce various notions of orientations and shadows, study some of their properties and list some open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T13:39:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coxeter group",
      "open questions",
      "orientation",
      "bruhat order",
      "end-alcoves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}