{
  "annotation_id": "7a7c7985-b279-4fcc-964a-8cc93c218e46",
  "date_created": "2026-03-02T18:01:28.590000Z",
  "date_modified": "2026-03-02T18:01:28.590000Z",
  "file_hash": "66832eb0df35e2ab0a72e9945183992afcbd22a201d41b3c0e50834b6e27c1ee",
  "private": false,
  "record": {
    "abstract": "We define a one-parameter family of two-sided coideals in U_q(gl(n)) and\nstudy the corresponding algebras of infinitesimally right invariant functions\non the quantum unitary group U_q(n). The Plancherel decomposition of these\nalgebras with respect to the natural transitive U_q(n)-action is shown to be\nthe same as in the case of a complex projective space. By computing the radial\npart of a suitable Casimir operator, we identify the zonal spherical functions\n(i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional\nirreducible representations) as Askey-Wilson polynomials containing two\ncontinuous and one discrete parameter. In certain limit cases, the zonal\nspherical functions are expressed as big and little q-Jacobi polynomials\ndepending on one discrete parameter.",
    "arxiv_id": "q-alg/9605017",
    "authors": [
      "M. S. Dijkhuizen",
      "M. Noumi"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "A family of quantum projective spaces and related q-hypergeometric   orthogonal polynomials",
    "url": "https://arxiv.org/abs/q-alg/9605017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d1f26339-1a66-4acb-954a-c57fd76a7dd5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}