{
  "id": "0707.1733",
  "version": "v1",
  "published": "2007-07-12T04:16:41.000Z",
  "updated": "2007-07-12T04:16:41.000Z",
  "title": "Cyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra",
  "authors": [
    "Toshiaki Shoji",
    "Kentaro Wada"
  ],
  "comment": "43 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $S$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $H_{n,r}$ of rank $n$, introduced by Dipper-James-Mathas. For each $p = (r_1, ..., r_g)$ such that $r_1 + ... + r_g = r$, we define a subalgebra $S^p$ of $S$ and its quotient algebra $\\bar S^p$. It is shown that $S^p$ is a standardly based algebra and $\\bar S^p$ is a cellular algebra. By making use of these algebras, we show that certain decomposition numbers for $S$ can be expressed as a product of decomposition numbers for cyclotomic $q$-Schur algebras associated to smaller Ariki_koike algebras $H_{n_k,r_k}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-12T04:16:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20C20",
      "20G05"
    ],
    "keywords": [
      "schur algebras",
      "ariki-koike algebra",
      "cyclotomic",
      "decomposition numbers",
      "quotient algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1733S"
    }
  }
}