{
  "id": "1402.5217",
  "version": "v1",
  "published": "2014-02-21T06:57:40.000Z",
  "updated": "2014-02-21T06:57:40.000Z",
  "title": "Lie Groups of Jacobi polynomials and Wigner d-matrices",
  "authors": [
    "E. Celeghini",
    "M. A. del Olmo",
    "M. A. Velasco"
  ],
  "comment": "21 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1307.7380",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A symmetry $SU(2,2)$ group in terms of ladder operators is presented for the Jacobi polynomials, $J_{n}^{(\\alpha,\\beta)}(x)$, and the Wigner $d_j$-matrices where the spins $j=n+(\\alpha+\\beta)/2$ integer and half-integer are considered together. A unitary irreducible representation of $SU(2,2)$ is constructed and subgroups of physical interest are discussed. The Universal Enveloping Algebra of $su(2,2)$ also allows to construct group structures $(SU(1,1), SO(3,2), Spin(3,2))$ whose representations separate integers and half-integers values of the spin $j$. Appropriate $L^2$--functions spaces are realized inside the support spaces of all these representations. Operators acting on these $L^2$-functions spaces belong thus to the corresponding Universal Enveloping Algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-21T06:57:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobi polynomials",
      "wigner d-matrices",
      "lie groups",
      "functions spaces belong",
      "representations separate integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1282314,
      "adsabs": "2014arXiv1402.5217C"
    }
  }
}