{
  "id": "1205.3520",
  "version": "v2",
  "published": "2012-05-15T21:53:08.000Z",
  "updated": "2013-05-31T18:37:50.000Z",
  "title": "Yang-Baxter equation, parameter permutations, and the elliptic beta integral",
  "authors": [
    "S. E. Derkachov",
    "V. P. Spiridonov"
  ],
  "comment": "43 pp., to appear in Russian Math. Surveys",
  "journal": "Russian Math. Surveys, 68 (2013), no. 6, 1027-1072",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We construct an infinite-dimensional solution of the Yang-Baxter equation (YBE) of rank 1 which is represented as an integral operator with an elliptic hypergeometric kernel acting in the space of functions of two complex variables. This R-operator intertwines the product of two standard L-operators associated with the Sklyanin algebra, an elliptic deformation of sl(2)-algebra. It is built from three basic operators $\\mathrm{S}_1, \\mathrm{S}_2$, and $\\mathrm{S}_3$ generating the permutation group of four parameters $\\mathfrak{S}_4$. Validity of the key Coxeter relations (including the star-triangle relation) is based on the elliptic beta integral evaluation formula and the Bailey lemma associated with an elliptic Fourier transformation. The operators $\\mathrm{S}_j$ are determined uniquely with the help of the elliptic modular double.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-31T18:37:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yang-baxter equation",
      "parameter permutations",
      "elliptic beta integral evaluation formula",
      "elliptic hypergeometric kernel",
      "elliptic fourier transformation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1070/RM2013v068n06ABEH004869",
      "journal": "Russian Mathematical Surveys",
      "year": 2013,
      "month": "Dec",
      "volume": 68,
      "number": 6,
      "pages": 1027
    },
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1114993,
      "adsabs": "2013RuMaS..68.1027D"
    }
  }
}