{
  "id": "1305.6162",
  "version": "v3",
  "published": "2013-05-27T10:01:52.000Z",
  "updated": "2015-01-09T14:25:34.000Z",
  "title": "Categorification of tensor powers of the vector representation of $U_q(\\mathfrak{gl}(1|1))$",
  "authors": [
    "Antonio Sartori"
  ],
  "comment": "This is a revised version, with many corrections and improvements. This article is part of the author's PhD thesis",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We consider the monoidal subcategory of finite dimensional representations of $U_q(\\mathfrak{gl}(1|1))$ generated by the vector representation, and we provide a diagram calculus for the intertwining operators, which allows to compute explicitly the canonical basis. We construct then a categorification of these representations and of the action of both $U_q(\\mathfrak{gl}(1|1))$ and the intertwining operators using subquotient categories of the BGG category $\\mathcal{O}(\\mathfrak{gl}_n)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-27T10:03:23.000Z",
      "comment": "The old paper has been split into two parts; this is now the first half of the old paper. This article is part of the author's PhD thesis",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-09T14:25:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B37",
      "20C08"
    ],
    "keywords": [
      "vector representation",
      "tensor powers",
      "categorification",
      "finite dimensional representations",
      "intertwining operators"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6162S"
    }
  }
}