{
  "annotation_id": "6c68e95f-51d1-470e-b2d3-283b057b39f1",
  "date_created": "2026-03-02T18:01:28.845000Z",
  "date_modified": "2026-03-02T18:01:28.845000Z",
  "file_hash": "31cd2a6c30a8853160de47206da0a961c7de40c4b5ad062b30dffd9c73b380fb",
  "private": false,
  "record": {
    "abstract": "We construct and study in detail various dual pairs acting on some Fock\nrepresentations between a finite dimensional Lie group and a completed infinite\nrank affine algebra associated to an infinite affine Cartan matrix. We give\nexplicit decompositions of a Fock representation into a direct sum of\nirreducible isotypic subspaces with respect to the action of a dual pair,\npresent explicit formulas for the common highest weight vectors and calculate\nthe corresponding highest weights. We further outline applications of these\ndual pairs to the study of tensor products of modules of such an infinite\ndimensional Lie algebra.",
    "arxiv_id": "q-alg/9710035",
    "authors": [
      "Weiqiang Wang"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Commun. Contemp. Math., Vol. 1 (1999) 155--199",
    "title": "Duality in infinite dimensional Fock representations",
    "url": "https://arxiv.org/abs/q-alg/9710035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "819aa006-9468-4a79-9bec-412b02b746d7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}