{
  "annotation_id": "4440255f-1e74-4f62-9955-7416f2ae7143",
  "date_created": "2026-03-02T18:01:28.598000Z",
  "date_modified": "2026-03-02T18:01:28.598000Z",
  "file_hash": "1545fb87d4bb42d3f4711e3ac5c76def0d91dd411d85a8696e4a85a500fd48ca",
  "private": false,
  "record": {
    "abstract": "In this paper, we introduce a new family of symmetric polynomials which\ndepends on a parameter r. They are defined by specifying certain of their\nzeros. For the parameter values 1/2, 1, and 2 they have an interpretation in\nterms of Capelli identities.\n  First, we give explicit formulas in some special cases. Then we show that the\npolynomials can also be defined in terms of difference equations. As a\ncorollary we obtain that their top homogeneous part is a Jack polynomial. This\nis used to give a new proof of the Pieri formula for Jack polynomials.",
    "arxiv_id": "q-alg/9610017",
    "authors": [
      "Friedrich Knop",
      "Siddhartha Sahi"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1155/S107379289600030X",
    "journal_ref": "Internat. Math. Res. Notices 1996, No. 10, 473-486",
    "title": "Difference equations and symmetric polynomials defined by their zeros",
    "url": "https://arxiv.org/abs/q-alg/9610017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9e59d7ff-3652-46ad-9b65-16a6ec6897ef",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}