{
  "id": "1612.02144",
  "version": "v1",
  "published": "2016-12-07T08:33:57.000Z",
  "updated": "2016-12-07T08:33:57.000Z",
  "title": "A $q$-series identity via the $\\mathfrak{sl}_3$ colored Jones polynomials for the $(2,2m)$-torus link",
  "authors": [
    "Wataru Yuasa"
  ],
  "comment": "11 pages, many TikZ pictures, 1 table",
  "categories": [
    "math.GT",
    "math.CO",
    "math.NT"
  ],
  "abstract": "The colored Jones polynomial is a $q$-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A $q$-series called a tail is obtained as the limit of the $\\mathfrak{sl}_2$ colored Jones polynomials $\\{J_n(K;q)\\}_n$ for some link $K$, for example, an alternating link. For the $\\mathfrak{sl}_3$ colored Jones polynomials, the existence of a tail is unknown. We give two explicit formulas of the tail of the $\\mathfrak{sl}_3$ colored Jones polynomials colored by $(n,0)$ for the $(2,2m)$-torus link. These two expressions of the tail provide an identity of $q$-series. This is a knot-theoretical generalization of the Andrews-Gordon identities for the Ramanujan false theta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-07T08:33:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "11P84",
      "05A30"
    ],
    "keywords": [
      "colored jones polynomial",
      "torus link",
      "series identity",
      "ramanujan false theta function",
      "simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}