{
  "id": "1902.07682",
  "version": "v1",
  "published": "2019-02-20T17:55:37.000Z",
  "updated": "2019-02-20T17:55:37.000Z",
  "title": "On $q$-Schur algebras corresponding to Hecke algebras of type B",
  "authors": [
    "Chun-Ju Lai",
    "Daniel K. Nakano",
    "Ziqing Xiang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to realize these $q$-Schur algebras as the duals of the $d$th graded components of certain graded coalgebras. Under suitable conditions a Morita equivalence theorem is proved that demonstrates that the representation theory reduces to the $q$-Schur algebra of type A. This enables the authors to address the questions of cellularity, quasi-hereditariness and representation type of these algebras. Later it is shown that these algebras realize the $1$-faithful quasi hereditary covers of the Hecke algebras of type B.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-20T17:55:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke algebras",
      "schur algebras corresponding",
      "coordinate algebra type construction",
      "morita equivalence theorem",
      "representation theory reduces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}