{
  "id": "1903.00274",
  "version": "v1",
  "published": "2019-03-01T12:56:05.000Z",
  "updated": "2019-03-01T12:56:05.000Z",
  "title": "Boundary matrices for the higher spin six vertex model",
  "authors": [
    "Vladimir V. Mangazeev",
    "Xilin Lu"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "nlin.SI"
  ],
  "abstract": "In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin $R$-matrix is associated with the affine quantum algebra $U_q(\\widehat{sl(2)})$. The explicit formulas for boundary $K$-matrices for spins $s=1/2,1$ are well known. We derive difference equations for the generating function of matrix elements of the $K$-matrix for any spin $s$ and solve them in terms of hypergeometric functions. As a result we derive the explicit formula for matrix elements of the $K$-matrix for arbitrary spin. In the lower- and upper- triangular cases, the $K$-matrix simplifies and reduces to simple products of $q$-Pochhammer symbols.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-01T12:56:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R50",
      "33D15"
    ],
    "keywords": [
      "vertex model",
      "boundary matrices",
      "explicit formula",
      "matrix elements",
      "affine quantum algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}