{
  "id": "0707.1753",
  "version": "v1",
  "published": "2007-07-12T09:04:06.000Z",
  "updated": "2007-07-12T09:04:06.000Z",
  "title": "On decomposition numbers with Jantzen filtration of cyclotomic $q$-Schur algebras",
  "authors": [
    "Kentaro Wada"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $\\Sc(\\vL)$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $\\He_{n,r}$, introduced by Dipper-James-Mathas. In this paper, we consider $v$-decomposition numbers of $\\Sc(\\vL)$, namely decomposition numbers with respect to the Jantzen filtrations of Weyl modules. We prove, as a $v$-analogue of the result obtained by Shoji-Wada, a product formula for $v$-decomposition numbers of $\\Sc(\\vL)$, which asserts that certain $v$-decomposition numbers are expressed as a product of $v$-decomposition numbers for various cyclotomic $q$-Schur algebras associated to Ariki-koike algebras $\\He_{n_i,r_i}$ of smaller rank. Moreover we prove a similar formula for $v$-decomposition numbers of $\\He_{n,r}$ by using a Schur functor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-12T09:04:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20C20",
      "20G05"
    ],
    "keywords": [
      "decomposition numbers",
      "jantzen filtration",
      "cyclotomic",
      "ariki-koike algebra",
      "schur functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1753W"
    }
  }
}