{
  "annotation_id": "221135d8-1a64-43cc-a5b3-e6381552eb41",
  "date_created": "2026-03-02T18:01:27.680000Z",
  "date_modified": "2026-03-02T18:01:27.680000Z",
  "file_hash": "3fc5f1070933287a55acdef7dcac260d6d6284fb232e75514aadfe044d3a983c",
  "private": false,
  "record": {
    "abstract": "We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a\nset of degree--lowering operators on the space of polynomials in $n$ variables.\nThis allows the construction of raising/lowering operators with a simple action\non non-symmetric Macdonald polynomials. A bilinear series of non-symmetric\nMacdonald polynomials is introduced as a $q$-analogue of the type $A$ Dunkl\nintegral kernel ${\\cal K}_A(x;y)$. The aforementioned operators are used to\nshow that the function satisfies $q$-analogues of the fundamental properties of\n${\\cal K}_A(x;y)$.",
    "arxiv_id": "q-alg/9701039",
    "authors": [
      "T. H. Baker",
      "P. J. Forrester"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "A $q$-analogue of the type $A$ Dunkl operator and integral kernel",
    "url": "https://arxiv.org/abs/q-alg/9701039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a351d648-c793-4fdf-974c-b3194ff26022",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}