{
  "id": "1307.7380",
  "version": "v1",
  "published": "2013-07-28T16:49:21.000Z",
  "updated": "2013-07-28T16:49:21.000Z",
  "title": "Jacobi polynomials and SU(2,2)",
  "authors": [
    "E. Celeghini",
    "M. A. del Olmo",
    "M. A. Velasco"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.GR",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir C_SU(2,2)=-3/2. As they determine also a base of square-integrable functions, the universal enveloping algebra of su(2,2) is homomorphic to the space of linear operators acting on the L^2 functions defined on (-1,+1) x Z x Z/2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-28T16:49:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobi polynomials",
      "linear operators",
      "ladder structure",
      "universal enveloping algebra",
      "quadratic casimir"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7380C"
    }
  }
}