{
  "annotation_id": "d82343cf-0dce-43ba-b2fc-2cd6497915f9",
  "date_created": "2026-03-02T18:01:24.964000Z",
  "date_modified": "2026-03-02T18:01:24.964000Z",
  "file_hash": "5c34a6602673252ddb8cf5499a052d1fc28878eeadf7ee7b4a4a41c13a9ee468",
  "private": false,
  "record": {
    "abstract": "In this paper we study modular tensor categories (braided rigid balanced\ntensor categories with additional finiteness and non-degeneracy conditions), in\nparticular, representations of quantum groups at roots of unity. We show that\nthe action of modular group on certain spaces of morphisms in MTC is unitary\nwith respect to the natural inner product on these spaces. In a special case of\ncategory based on representations of the quantum group U_q sl_n at roots of\nunity we show that in some of these spaces of morphisms (for U_q sl_2, in all\nof them) the action of modular group can be written in terms of values of\nMacdonald\u0027s polynomials of type A at roots of unity. This gives identities for\nthese special values, both known before (symmetry identity) and new ones.\n  The paper contains a detailed exposition of the theory of modular categories\nas well as construction of modular categories from representation of quantum\ngroups at roots of unity",
    "arxiv_id": "q-alg/9508017",
    "authors": [
      "Alexander Kirillov Jr."
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "On inner product in modular tensor categories. I",
    "url": "https://arxiv.org/abs/q-alg/9508017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "873e2314-d4ba-47af-851e-d9fc8f4e6e6b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}