{
  "annotation_id": "9306833b-9671-4023-82bc-9834329644fa",
  "date_created": "2026-03-02T18:01:28.590000Z",
  "date_modified": "2026-03-02T18:01:28.590000Z",
  "file_hash": "dfaa3fb3276c0315008dddddd48b4aac0d9c3e802e4eb609f647f66dafb4fab2",
  "private": false,
  "record": {
    "abstract": "The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials\nas overlap coefficients in the positive discrete series representations of the\nLie algebra su(1,1) and the Clebsch-Gordan decomposition leads to\ngeneralisations of the convolution identities for these polynomials. Using the\nRacah coefficients convolution identities for continuous Hahn, Hahn and Jacobi\npolynomials are obtained. From the quantised universal enveloping algebra for\nsu(1,1) convolution identities for the Al-Salam and Chihara polynomials and the\nAskey-Wilson polynomials are derived by using the Clebsch-Gordan and Racah\ncoefficients. For the quantised universal enveloping algebra for su(2) q-Racah\npolynomials are interpreted as Clebsch-Gordan coefficients, and the\nlinearisation coefficients for a two-parameter family of Askey-Wilson\npolynomials are derived.",
    "arxiv_id": "q-alg/9607010",
    "authors": [
      "H. T. Koelink",
      "J. Van der Jeugt"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Convolutions for orthogonal polynomials from Lie and quantum algebra   representations",
    "url": "https://arxiv.org/abs/q-alg/9607010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3e6e0160-a759-4941-bc22-d475310d9a8b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}