{
  "annotation_id": "97c61109-c333-447f-aa8a-c36473b64a9d",
  "date_created": "2026-03-02T18:01:28.591000Z",
  "date_modified": "2026-03-02T18:01:28.591000Z",
  "file_hash": "c4bd61ddadb0ca14bbd7c4d3bb47fd55191edf078ee6c02073dc076a2d842c0b",
  "private": false,
  "record": {
    "abstract": "We extend some results about shifted Schur functions to the general context\nof shifted Macdonald polynomials. We obtain two explicit formulas for these\npolynomials: a $q$-integral representation and a combinatorial formula. Our\nmain tool is a $q$-integral representation for ordinary Macdonald polynomials.\nWe also discuss duality for shifted Macdonald polynomials and Jack degeneration\nof these polynomials.",
    "arxiv_id": "q-alg/9605013",
    "authors": [
      "Andrei Okounkov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "(Shifted) Macdonald Polynomials: q-Integral Representation and   Combinatorial Formula",
    "url": "https://arxiv.org/abs/q-alg/9605013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "aa0d9684-9371-4684-af18-21d4348f8ac5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}