{
  "annotation_id": "d826d863-7407-4778-a9c2-e8698726858c",
  "date_created": "2026-03-02T18:01:28.149000Z",
  "date_modified": "2026-03-02T18:01:28.149000Z",
  "file_hash": "a9c93dd721df2a6b65077d7dd80f45276576c682b3e771903e6ee808738107e5",
  "private": false,
  "record": {
    "abstract": "This paper considers Darboux transformations of a bispectral operator which\npreserve its bispectrality. A sufficient condition for this to occur is given,\nand applied to the case of generalized Airy operators of arbitrary order $r\u003e1$.\nAs a result, the bispectrality of a large family of algebras of rank $r$ is\ndemonstrated. An involution on these algebras is exhibited which exchanges the\nrole of spatial and spectral parameters, generalizing Wilson\u0027s rank one\nbispectral involution. Spectral geometry and the relationship to the Sato\ngrassmannian are discussed.",
    "arxiv_id": "q-alg/9606018",
    "authors": [
      "Alex Kasman",
      "Mitchell Rothstein"
    ],
    "categories": [
      "q-alg",
      "math.QA",
      "nlin.SI",
      "solv-int"
    ],
    "doi": "10.1016/S0167-2789(96)00208-4",
    "title": "Bispectral Darboux Transformations: The Generalized Airy Case",
    "url": "https://arxiv.org/abs/q-alg/9606018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "864befe6-5625-44ed-a47c-41fca0cd4e10",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}