{
  "annotation_id": "9f35922c-14f3-42a4-aa61-982f71d8d5f7",
  "date_created": "2026-03-02T18:01:28.474000Z",
  "date_modified": "2026-03-02T18:01:28.474000Z",
  "file_hash": "d3b6c475b72034c552d48d450a53914199825494e29932aa409f1cc28d6df8aa",
  "private": false,
  "record": {
    "abstract": "We define a family of symmetric and a family of non-symmetric polynomials in\nterms of vanishing conditions. These families depend on two paramters, q and t.\nTheir main feature is that they consist of non-homogeneous polynomials. The\nsymmetric polynomials form the quantized version of polynomials occuring in the\ncontext of generalized Capelli identities. We show that these quantum Capelli\npolynomials are also characterized by q-difference equations. More precisely,\nthey are eigenfunctions of Cherednik type operators and transform under an\naffine Hecke algebra. Thus, we are able to identify their top homogeneous\ncomponent as a Macdonald polynomial (symmetric or non-symmetric, respectively).",
    "arxiv_id": "q-alg/9603028",
    "authors": [
      "Friedrich Knop"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Comment. Math. Helv. 72 (1997), 84-100",
    "title": "Symmetric and non-symmetric quantum Capelli polynomials",
    "url": "https://arxiv.org/abs/q-alg/9603028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f463dc1f-1e9f-479e-b612-6cf0eb6af924",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}