{
  "annotation_id": "99cb498b-617e-459b-8580-9f9325391d14",
  "date_created": "2026-03-02T18:01:28.351000Z",
  "date_modified": "2026-03-02T18:01:28.351000Z",
  "file_hash": "0f2d9f56420e5507472da2486c3f994d8aee8cbfdbc0927d94fb482f2eb888ee",
  "private": false,
  "record": {
    "abstract": "We introduce the quantum multi-Schur functions, quantum factorial Schur\nfunctions and quantum Macdonald polynomials. We prove that for restricted\nvexillary permutations the quantum double Schubert polynomial coincides with\nsome quantum multi-Schur function and prove a quantum analog of the\nNagelsbach-Kostka and Jacobi-Trudi formulae for the quantum double Schubert\npolynomials in the case of Grassmannian permutations. We prove, also, an analog\nof the Billey-Jockusch-Stanley formula for quantum Schubert polynomials.\nFinally we formulate two conjectures about the structure of quantum double and\nquantum Schubert polynomials for 321-avoiding permutations.",
    "arxiv_id": "q-alg/9701005",
    "authors": [
      "Anatol N. Kirillov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Quantum Schubert polynomials and quantum Schur functions",
    "url": "https://arxiv.org/abs/q-alg/9701005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "95cb0586-729f-4d6e-b983-f8cd2b7db95e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}