{
  "id": "math/0302342",
  "version": "v1",
  "published": "2003-02-27T16:36:30.000Z",
  "updated": "2003-02-27T16:36:30.000Z",
  "title": "Laguerre functions and representations of su(1,1)",
  "authors": [
    "Wolter Groenevelt"
  ],
  "comment": "19 pages",
  "journal": "Indag. Math. (N.S.) 14 (2003), no. 3-4, 329-352",
  "categories": [
    "math.CA",
    "math.RT"
  ],
  "abstract": "Spectral analysis of a certain doubly infinite Jacobi operator leads to orthogonality relations for confluent hypergeometric functions, which are called Laguerre functions. This doubly infinite Jacobi operator corresponds to the action of a parabolic element of the Lie algebra $\\mathfrak{su}(1,1)$. The Clebsch-Gordan coefficients for the tensor product representation of a positive and a negative discrete series representation of $\\mathfrak{su}(1,1)$ are determined for the parabolic bases. They turn out to be multiples of Jacobi functions. From the interpretation of Laguerre polynomials and functions as overlap coefficients, we obtain a product formula for the Laguerre polynomials, given by a discontinuous integral over Laguerre functions, Jacobi functions and continuous dual Hahn polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-27T16:36:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "laguerre functions",
      "doubly infinite jacobi operator corresponds",
      "laguerre polynomials",
      "jacobi functions",
      "confluent hypergeometric functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2342G"
    }
  }
}