{
  "annotation_id": "d2f539af-566e-4d17-bfb2-68061c985d28",
  "date_created": "2026-03-02T18:02:41.047000Z",
  "date_modified": "2026-03-02T18:02:41.047000Z",
  "file_hash": "be120e25c51eb4da615a0ac29df5bd3869781675b005e0427159878236b8f09a",
  "private": false,
  "record": {
    "abstract": "It has been shown that the Cartan subalgebra of $W_{\\infty}$- algebra is the\nspace of the two-variable, definite-parity polynomials. Explicit expressions of\nthese polynomials, and their basic properties are presented. Also has been\nshown that they carry the infinite dimensional irreducible representation of\nthe $su(1,1)$ algebra having the spectrum bounded from below. A realization of\nthis algebra in terms of difference operators is also obtained. For particular\nvalues of the ordering parameter $s$ they are identified with the classical\northogonal polynomials of a discrete variable, such as the Meixner,\nMeixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable $s$\nthey satisfy a second order eigenvalue equation of hypergeometric type. Exact\nscattering states with zero energy for a family of potentials are expressed in\nterms of these polynomials. It has been put forward that it is the\n\\.{I}n\\\"{o}n\\\"{u}-Wigner contraction and its inverse that form bridge between\nthe difference and differential calculus.",
    "arxiv_id": "quant-ph/9712026",
    "authors": [
      "A. Ver\u00e7in"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532295",
    "journal_ref": "J.Math.Phys. 39 (1998) 2418-2427",
    "title": "Ordered Products, $W_{\\infty}$-Algebra, and Two-Variable,   Definite-Parity, Orthogonal Polynomials",
    "url": "https://arxiv.org/abs/quant-ph/9712026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a6349a44-6951-4aaf-ac08-2d195c14e6c8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}