{
  "id": "1901.02323",
  "version": "v1",
  "published": "2019-01-08T14:35:08.000Z",
  "updated": "2019-01-08T14:35:08.000Z",
  "title": "The ABC of p-Cells",
  "authors": [
    "Lars Thorge Jensen"
  ],
  "comment": "36 pages, best viewed in colour",
  "categories": [
    "math.RT",
    "math.CO",
    "math.GR"
  ],
  "abstract": "Parallel to the very rich theory of Kazhdan-Lusztig cells in characteristic $0$, we try to build a similar theory in positive characteristic. We study cells with respect to the $p$-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see arXiv:1510.01556(2)). Our main technical tool are the star-operations introduced by Kazhdan-Lusztig which have interesting numerical consequences for the $p$-canonical basis. As an application, we explicitely describe $p$-cells in finite type $A$ (i.e. for symmetric groups) using the Robinson-Schensted correspondence. Moreover, we show that Kazhdan-Lusztig cells in finite types $B$ and $C$ decompose into $p$-cells for $p > 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-08T14:35:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20B05",
      "05E10"
    ],
    "keywords": [
      "kazhdan-lusztig cells",
      "finite type",
      "crystallographic coxeter system",
      "canonical basis",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}