{
  "id": "math/0506403",
  "version": "v4",
  "published": "2005-06-20T15:41:51.000Z",
  "updated": "2012-11-10T09:00:10.000Z",
  "title": "The quantum $\\mathfrak{sl}(n,\\mathbb{C})$ representation theory and its applications",
  "authors": [
    "Myeong-Ju Jeong",
    "Dongseok Kim"
  ],
  "comment": "19 pages, 18 figures",
  "journal": "J. Korean Math. Soc. 49 (2012), No. 5, pp. 993-1015",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "In this paper, we study the quantum $\\mathfrak{sl}(n)$ representation category using the web space. Specially, we extend $\\mathfrak{sl}(n)$ web space for $n\\ge 4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of $\\mathfrak{sl}(n)$. Moreover, we correct the false conjecture \\cite{PS:superiod} given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial $(n = 0)$ and Jones polynomial $(n = 2)$ and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-11-10T09:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "representation theory",
      "homfly polynomial",
      "application",
      "web space",
      "variable polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6403J"
    }
  }
}