{
  "id": "1405.4726",
  "version": "v3",
  "published": "2014-05-19T13:59:00.000Z",
  "updated": "2014-08-19T18:54:06.000Z",
  "title": "The nineteen-vertex model and alternating sign matrices",
  "authors": [
    "Christian Hagendorf"
  ],
  "comment": "28 pages, 6 figures; v2: corrected misprint in arXiv metadata (title); v3: revised version",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvector is computed by means of the algebraic Bethe ansatz, and both a simple component and its square norm are expressed in terms of the Izergin-Korepin determinant. In the homogeneous limit, the vector coincides with a supersymmetry singlet of the twisted spin-one XXZ chain. It is shown that in a natural polynomial normalisation scheme its square norm and the simple component coincide with generating functions for weighted enumeration of alternating sign matrices.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-19T18:54:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating sign matrices",
      "nineteen-vertex model",
      "natural polynomial normalisation scheme",
      "square norm",
      "diagonal twisted boundary conditions possesses"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2015/01/P01017",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2015,
      "month": "Jan",
      "volume": 2015,
      "number": 1,
      "pages": "01017"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JSMTE..01..017H"
    }
  }
}