{
  "id": "1411.4125",
  "version": "v1",
  "published": "2014-11-15T08:51:09.000Z",
  "updated": "2014-11-15T08:51:09.000Z",
  "title": "A $q$-analogue of derivations on the tensor algebra and the $q$-Schur--Weyl duality",
  "authors": [
    "Minoru Itoh"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori--Hecke algebra type $A$ of infinite degree. Namely this algebra can be regarded as a natural mix of these two algebras. Moreover, we can consider natural \"derivations\" on this algebra. Using these derivations, we can easily prove the $q$-Schur--Weyl duality (the duality between the quantum enveloping algebra of the general linear Lie algebra and the Iwahori--Hecke algebra of type $A$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-15T08:51:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A72",
      "17B37",
      "20C08"
    ],
    "keywords": [
      "schur-weyl duality",
      "derivations",
      "general linear lie algebra",
      "ordinary tensor algebra",
      "iwahori-hecke algebra type"
    ],
    "publication": {
      "doi": "10.1007/s11005-015-0793-7",
      "journal": "Letters in Mathematical Physics",
      "year": 2015,
      "month": "Oct",
      "volume": 105,
      "number": 10,
      "pages": 1467
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015LMaPh.105.1467I"
    }
  }
}