{
  "id": "math/0510457",
  "version": "v1",
  "published": "2005-10-21T10:39:02.000Z",
  "updated": "2005-10-21T10:39:02.000Z",
  "title": "On decomposition numbers of the cyclotomic q-Schur algebras",
  "authors": [
    "Nobuharu Sawada"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $S(\\Lambda)$ be the cyclotomic q-Schur algebra associated to the Ariki-Koike algebra $H$. We construct a certain subalgebra $S^0(\\Lambda)$ of $S(\\Lambda)$, and show that it is a standardly based algebra in the sense of Du and Rui. $S^0(\\Lambda)$ has a natural quotient $\\bar{S^0}(\\Lambda)$, which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra $H^{\\flat}$ is defined, $\\bar{S^0}(\\Lambda)$ coincides with the cyclotomic q-Schur algebra associated to $H^{\\flat}$. In this paper, we discuss a relationship among the decomposition numbers of $S(\\Lambda)$, $S^0(\\Lambda)$ and $\\bar{S^0}(\\Lambda)$. In particular, we show that some important part of the decomposition matrix of $S(\\Lambda)$ coincides with a part of the decomposition matrix of $\\bar{S^0}(\\Lambda)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-21T10:39:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20C20"
    ],
    "keywords": [
      "decomposition numbers",
      "cyclotomic q-schur algebra",
      "decomposition matrix",
      "important part",
      "natural quotient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10457S"
    }
  }
}