{
  "id": "1306.6599",
  "version": "v3",
  "published": "2013-06-27T18:39:32.000Z",
  "updated": "2014-04-15T04:49:35.000Z",
  "title": "Vector Polynomials and a Matrix Weight Associated to Dihedral Groups",
  "authors": [
    "Charles F. Dunkl"
  ],
  "journal": "SIGMA 10 (2014), 044, 23 pages",
  "doi": "10.3842/SIGMA.2014.044",
  "categories": [
    "math.CA"
  ],
  "abstract": "The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the normalizing constant. An orthogonal basis for the homogeneous harmonic polynomials is constructed. The coefficients of these polynomials are found to be balanced terminating $_4F_3$-series.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-15T04:49:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C52",
      "20F55",
      "33C45"
    ],
    "keywords": [
      "dihedral group",
      "vector polynomials",
      "boundary value problem",
      "matrix weight function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2014,
      "month": "Apr",
      "volume": 10,
      "pages": "044"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014SIGMA..10..044D"
    }
  }
}