{
  "annotation_id": "3b75fbfb-7b54-4273-9ffe-502320ece388",
  "date_created": "2026-03-02T18:01:27.667000Z",
  "date_modified": "2026-03-02T18:01:27.667000Z",
  "file_hash": "0efacb01422acf6bfd2e7f4bb1c50a3b04adeb9dae1260dd52d5ffc9c10145e3",
  "private": false,
  "record": {
    "abstract": "We prove that the scalar and $2\\times 2$ matrix differential operators which\npreserve the simplest scalar and vector-valued polynomial modules in two\nvariables have a fundamental Lie algebraic structure. Our approach is based on\na general graphical method which does not require the modules to be irreducible\nunder the action of the corresponding Lie (super)algebra. This method can be\ngeneralized to modules of polynomials in an arbitrary number of variables. We\ngive generic examples of partially solvable differential operators which are\nnot Lie algebraic. We show that certain vector-valued modules give rise to new\nrealizations of finite-dimensional Lie superalgebras by first-order\ndifferential operators.",
    "arxiv_id": "q-alg/9612027",
    "authors": [
      "Federico Finkel",
      "Niky Kamran"
    ],
    "categories": [
      "q-alg",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "journal_ref": "Adv. Appl. Math., 20 (1998) 300-322",
    "title": "The Lie Algebraic Structure of Differential Operators Admitting   Invariant Spaces of Polynomials",
    "url": "https://arxiv.org/abs/q-alg/9612027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fed59de4-0c9a-4ffe-88b3-cb9ab78ea6c0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}