{
  "annotation_id": "b1b888e3-3697-4c79-93b7-e1354ebfe9ae",
  "date_created": "2026-03-02T18:01:27.865000Z",
  "date_modified": "2026-03-02T18:01:27.865000Z",
  "file_hash": "ef1971ec63a9ab14f7afb5f6d31ab24c10d921a96de9f3d8c3da3b69f9cd8688",
  "private": false,
  "record": {
    "abstract": "A weight function which $q$-generalizes the ground state wave function of the\nmulti-component Calogero-Sutherland quantum many body system is introduced.\nConjectures, and some proofs in special cases, are given for a constant term\nidentity involving this function. A Gram-Schmidt procedure with respect to the\ninner product associated with the weight function is used to define orthogonal\npolynomials in one of the components, which are conjectured to be the Macdonald\npolynomials $P_\\kappa(w_1,\\dots,w_{N_0};qt^p,t)$, and a proof is given in a\nspecial case. Conjectures are also given for an adjoint property of the\nMacdonald operator with respect to the inner product associated with the weight\nfunction, and the normalization of the Macdonald polynomial with respect to the\nsame inner product.",
    "arxiv_id": "q-alg/9603005",
    "authors": [
      "T. H. Baker",
      "P. J. Forrester"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Generalized weight functions and the Macdonald polynomials",
    "url": "https://arxiv.org/abs/q-alg/9603005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7422c724-7294-4bf4-971b-862ecb1cf3af",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}