{
  "id": "1401.6494",
  "version": "v2",
  "published": "2014-01-25T04:02:27.000Z",
  "updated": "2014-06-10T03:39:28.000Z",
  "title": "On the Yang-Baxter equation for the six-vertex model",
  "authors": [
    "Vladimir V. Mangazeev"
  ],
  "comment": "25 pages, 1 figure",
  "journal": "Nucl Physics, B, v. 882, p. 70-96 (2014)",
  "doi": "10.1016/j.nuclphysb.2014.02.019",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA"
  ],
  "abstract": "In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of the corresponding 3D lattice model. As a result, we obtain a new expression for the higher spin $R$-matrix associated with the affine quantum algebra $U_q(\\widehat{sl(2)})$. In the simplest case of the spin $s=1/2$ this $R$-matrix naturally reduces to the $R$-matrix of the 6-vertex model. Taking a special limit in our construction we also obtain new formulas for the $Q$-operators acting in the representation space of arbitrary (half-)integer spin. Remarkably, this construction can be naturally extended to any complex values of spin $s$. We also give all functional equations satisfied by the transfer-matrices and $Q$-operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-10T03:39:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yang-baxter equation",
      "six-vertex model",
      "higher spin generalizations",
      "affine quantum algebra",
      "corresponding 3d lattice model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Nuclear Physics B",
      "year": 2014,
      "month": "May",
      "volume": 882,
      "pages": 70
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1278894,
      "adsabs": "2014NuPhB.882...70M"
    }
  }
}