{
  "annotation_id": "b7005ef4-105b-4306-acdd-b5558d742549",
  "date_created": "2026-03-02T18:01:28.417000Z",
  "date_modified": "2026-03-02T18:01:28.417000Z",
  "file_hash": "2695ab7fec766f996a70439629ec61c91400e956928d1015ca467102661d4abe",
  "private": false,
  "record": {
    "abstract": "We introduce a tensor category O_+ (resp. O_{-}) of certain modules of\ngl_{\\infty} with non-negative (resp. non-positive) integral central charges\nwith the usual tensor product. We also introduce a tensor category O_f\nconsisting of certain modules over GL(N) for all N. We show that the tensor\ncategories O_+, O_{-} and O_f are semisimple abelian and all equivalent to each\nother. We give a formula to decompose a tensor product of two modules in each\nof these categories. We also introduce a tensor category O^w of certain modules\nover W_{1 +\\infty} with non-negative integral central charges. We show that O^w\nis semisimple abelian and give an explicit formula to decompose a tensor\nproduct of two modules in O^w.",
    "arxiv_id": "q-alg/9709034",
    "authors": [
      "Weiqiang Wang"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Dual pairs and tensor categories of modules over Lie algebras   gl_{\\infty} and W_{1 +\\infty}",
    "url": "https://arxiv.org/abs/q-alg/9709034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "18579226-4e64-41ed-9891-e91ebdb83140",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}