{
  "annotation_id": "40ddf9ce-c06f-44ee-a6df-8d9ad03f0964",
  "date_created": "2026-03-02T18:01:28.581000Z",
  "date_modified": "2026-03-02T18:01:28.581000Z",
  "file_hash": "a2fb98f95657f01b853bfc632e808e218c40ba0c7c7887e88e6b1449801cbced",
  "private": false,
  "record": {
    "abstract": "We study certain $q$-difference raising operators for Macdonald polynomials\n(of type $A_{n-1}$) which are originated from the $q$-difference-reflection\noperators introduced in our previous paper. These operators can be regarded as\na $q$-difference version of the raising operators for Jack polynomials\nintroduced by L.Lapointe and L.Vinet. As an application of our $q$-difference\nraising operators we give an elementary proof of the integrality of the double\nKostka coefficients which had been conjectured I.G. Macdonald. We also\ndetermine their quasi-classical limits, which give rise to (differental)\nraising operators for Jack polynomials.",
    "arxiv_id": "q-alg/9605005",
    "authors": [
      "Anatol N. Kirillov",
      "Masatoshi Noumi"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "$q$-Difference raising operators for Macdonald polynomials and the   integrality of transition coefficients",
    "url": "https://arxiv.org/abs/q-alg/9605005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "503a2584-f471-472e-9c48-8bfec38e8e6f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}