{
  "annotation_id": "67415cb7-976e-48d4-b23a-874a8cc37224",
  "date_created": "2026-03-02T18:01:27.798000Z",
  "date_modified": "2026-03-02T18:01:27.798000Z",
  "file_hash": "808192eab927aaa02de5300da0b9ab2aa50e0b2b422cd161c8cba31b53a4cf4a",
  "private": false,
  "record": {
    "abstract": "We study the Poincar\\\u0027e series of the quantum spaces associated to a Hecke\noperator, i.e., a Yang-Baxter operator satisfying the equation $(x+1)(x-q)=0$.\nThe Poincar\\\u0027e series of the corresponding matrix bialgebra is also considered.\nUsing an old result on Poly\\\u0027a frequency sequence, we show that the Poincar\\\u0027e\nseries of quantum spaces are always rational functions having negative roots\nand positive poles. In particular, we show that the rank of an even Hecke\noperator should be rational functions having negative roots and positive poles.\nIn particular, we show that the rank of an even Hecke operator should be\ngreater than the dimension of the vector space it is acting on.",
    "arxiv_id": "q-alg/9711020",
    "authors": [
      "Phung Ho Hai"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Acta Math. Vietnamica, 24:2(1999), 235-246",
    "title": "Poincar\\\u0027e Series of Quantum Spaces Associated to Hecke Operators",
    "url": "https://arxiv.org/abs/q-alg/9711020"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cd35d872-f30b-44a3-8b83-8d5d859b0159",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}