{
  "id": "0812.0063",
  "version": "v1",
  "published": "2008-11-29T09:24:48.000Z",
  "updated": "2008-11-29T09:24:48.000Z",
  "title": "Some Orthogonal Polynomials in Four Variables",
  "authors": [
    "Charles F. Dunkl"
  ],
  "comment": "This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 4 (2008), 082, 9 pages",
  "doi": "10.3842/SIGMA.2008.082",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of polynomials of 4 variables with 2 parameters. There is an associated quantum Calogero-Sutherland model of 4 identical particles on the line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-29T09:24:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal polynomials",
      "associated quantum calogero-sutherland model",
      "isomorphic image",
      "symmetric group",
      "orthogonal basis"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2008,
      "month": "Nov",
      "volume": 4,
      "pages": "082"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008SIGMA...4..082D"
    }
  }
}