{
  "id": "0802.1408",
  "version": "v3",
  "published": "2008-02-11T11:07:11.000Z",
  "updated": "2008-10-28T23:39:05.000Z",
  "title": "Generalized induction of Kazhdan-Lusztig cells",
  "authors": [
    "Jeremie Guilhot"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Following Lusztig, we consider a Coxeter group $W$ together with a weight function. Geck showed that the Kazhdan-Lusztig cells of $W$ are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of $W$ which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of a certain finite parabolic subgroup of $W$ are cells in the whole group, and we decompose the affine Weyl group $\\tilde{G}_{2}$ into left and two-sided cells for a whole class of weight functions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-28T23:39:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kazhdan-lusztig cells",
      "generalized induction",
      "weight function",
      "affine weyl group",
      "finite parabolic subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.1408G"
    }
  }
}