{
  "annotation_id": "192db9f3-33bc-47a9-9d13-936f18b551f1",
  "date_created": "2026-03-02T18:01:28.636000Z",
  "date_modified": "2026-03-02T18:01:28.636000Z",
  "file_hash": "f2a7d318147ab74ab98838e32e156f6a55ea669ee1a712ab6d7dbc99398ee300",
  "private": false,
  "record": {
    "abstract": "We announce a systematic way for constructing bispectral algebras of\ncommuting differential operators of any rank N. It enables us to obtain all\npreviously known classes and examples of bispectral operators. Moreover, we\ngive a representation-theoretic explanation of the results including those of\nDuistermaat and Gr\\\"unbaum. The manifold of bispectral operators of any order\nis preserved by an hierarchy of symmetries. We point out that our methods\nprovide a completely algorithmic procedure for obtaining bispectral algebras.\nWe conjecture that the class built in the present paper exhausts all bispectral\nscalar operators.\n  The proofs and details appeared in our preprints hep-th/9510211,\nq-alg/9602010, q-alg/9602011, q-alg/9602012.",
    "arxiv_id": "q-alg/9601017",
    "authors": [
      "B. Bakalov",
      "E. Horozov",
      "M. Yakimov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Highest weight modules of W_{1+infty}, Darboux transformations and the   bispectral problem",
    "url": "https://arxiv.org/abs/q-alg/9601017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0df84715-9405-4ca8-953d-9c9690f00c74",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}