{
  "annotation_id": "c2274c01-3b40-4414-b069-6219546c1a4f",
  "date_created": "2026-03-02T18:01:27.609000Z",
  "date_modified": "2026-03-02T18:01:27.609000Z",
  "file_hash": "1bc1e2cbb6810a5a8eca0f970d216f1cb2854ac4570fa2ae5912e212e5e0a78f",
  "private": false,
  "record": {
    "abstract": "The representation theory of deformed oscillator algebras, defined in terms\nof an arbitrary function of the number operator~$N$, is developed in terms of\nthe eigenvalues of a Casimir operator~$C$. It is shown that according to the\nnature of the $N$ spectrum, their unitary irreducible representations may fall\ninto one out of four classes, some of which contain bosonic, fermionic or\nparafermionic Fock-space representations as special cases. The general theory\nis illustrated by classifying the unitary irreducible representations of the\nArik-Coon, Chaturvedi-Srinivasan, and Tamm-Dancoff oscillator algebras, which\nmay be derived from the boson one by the recursive minimal-deformation\nprocedure of Katriel and Quesne. The effects on non-Fock-space representations\nof the minimal deformation and of the quommutator-commutator transformation,\nconsidered in such a procedure, are studied in detail.",
    "arxiv_id": "q-alg/9605041",
    "authors": [
      "C. Quesne",
      "N. Vansteenkiste"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "journal_ref": "Helv.Phys.Acta 69 (1996) 141",
    "title": "Representation theory of deformed oscillator algebras",
    "url": "https://arxiv.org/abs/q-alg/9605041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "24b824e5-5131-424b-887b-ba0db2226f98",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}