{
  "id": "1302.4272",
  "version": "v3",
  "published": "2013-02-18T13:58:43.000Z",
  "updated": "2013-09-13T03:52:36.000Z",
  "title": "A cellular basis of the $q$-Brauer algebra related with Murphy bases of the Hecke algebras",
  "authors": [
    "Dung Tien Nguyen"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "A new basis of the $q$-Brauer algebra is introduced, which is a lift of Murphy bases of Hecke algebras of symmetric groups. This basis is a cellular basis in the sense of Graham and Lehrer. Subsequently, using combinatorial language we prove that the non-isomorphic simple $q$-Brauer modules are indexed by the $e(q^2)$-restricted partitions of $n-2k$ where $k$ is an integer, $0 \\le k \\le [n/2]$. When the $q$-Brauer algebra has low-dimension a criterion of semisimplicity is given, which is used to show that the $q$-Brauer algebra is in general not isomorphic to the BMW-algebra.}",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-13T03:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G30"
    ],
    "keywords": [
      "murphy bases",
      "brauer algebra",
      "cellular basis",
      "hecke algebras",
      "symmetric groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4272T"
    }
  }
}