{
  "id": "1302.3632",
  "version": "v2",
  "published": "2013-02-14T21:17:50.000Z",
  "updated": "2013-06-12T05:14:40.000Z",
  "title": "Vector-Valued Polynomials and a Matrix Weight Function with $B_2$-Action. II",
  "authors": [
    "Charles F. Dunkl"
  ],
  "journal": "SIGMA 9 (2013), 043, 11 pages",
  "doi": "10.3842/SIGMA.2013.043",
  "categories": [
    "math.CA"
  ],
  "abstract": "This is a sequel to [SIGMA 9 (2013), 007, 23 pages, arXiv:1210.1177], in which there is a construction of a $2\\times2$ positive-definite matrix function $K (x)$ on $\\mathbb{R}^{2}$. The entries of $K(x)$ are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group $W(B_2)$ (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: $k_{0}$, $k_{1}$. In the previous paper $K$ is determined up to a scalar, namely, the normalization constant. The conjecture stated there is proven in this note. An asymptotic formula for a sum of $_{3}F_{2}$-type is derived and used for the proof.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-12T05:14:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C52",
      "33C20"
    ],
    "keywords": [
      "matrix weight function",
      "vector-valued polynomials",
      "rational cherednik algebra",
      "positive-definite matrix function",
      "gaussian inner product"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2013,
      "month": "Jun",
      "volume": 9,
      "pages": "043"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013SIGMA...9..043D"
    }
  }
}