{
  "annotation_id": "7a5de8da-5c80-457b-ab4d-2ca9d2dca1bb",
  "date_created": "2026-03-02T18:01:28.408000Z",
  "date_modified": "2026-03-02T18:01:28.408000Z",
  "file_hash": "d155c4fda369a6f327eba8028686a6c3854b1f3712a7e19d9e1602cd78c1c6c8",
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  "record": {
    "abstract": "In this paper we study the asymptotic behavior of the Jack rational functions\nas the number of variables grows to infinity. Our results generalize the\nresults of A. Vershik and S. Kerov obtained in the Schur function case\n(theta=1). For theta=1/2,2 our results describe approximation of the spherical\nfunctions of the infinite-dimensional symmetric spaces $U(\\infty)/O(\\infty)$\nand $U(2\\infty)/Sp(\\infty)$ by the spherical functions of the corresponding\nfinite-dimensional symmetric spaces.",
    "arxiv_id": "q-alg/9709011",
    "authors": [
      "Andrei Okounkov",
      "Grigori Olshanski"
    ],
    "categories": [
      "q-alg",
      "cond-mat",
      "hep-th",
      "math.QA",
      "nlin.SI",
      "solv-int"
    ],
    "journal_ref": "Intern. Math. Research Notices 1998, no. 13, 641-682",
    "title": "Asymptotics of Jack polynomials as the number of variables goes to   infinity",
    "url": "https://arxiv.org/abs/q-alg/9709011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "de35e638-a77e-4a24-b6e8-ea01cdd24037",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}