{
  "annotation_id": "4bd0aac4-0985-424a-8662-ace778f17359",
  "date_created": "2026-03-02T18:01:28.648000Z",
  "date_modified": "2026-03-02T18:01:28.648000Z",
  "file_hash": "da012bbfc2284da69523d31b83ca52d70b831fa7045cdc592c068d39b791b292",
  "private": false,
  "record": {
    "abstract": "The representation theory of the generalized deformed oscillator algebras\n(GDOA\u0027s) is developed. GDOA\u0027s are generated by the four operators\n${1,a,a^{\\dag},N}$. Their commutators and Hermiticity properties are those of\nthe boson oscillator algebra, except for $[a, a^{\\dag}]_q = G(N)$, where\n$[a,b]_q = a b - q b a$ and $G(N)$ is a Hermitian, analytic function. The\nunitary irreductible representations are obtained by means of a Casimir\noperator $C$ and the semi-positive operator $a^{\\dag} a$. They may belong to\none out of four classes: bounded from below (BFB), bounded from above (BFA),\nfinite-dimentional (FD), unbounded (UB). Some examples of these different types\nof unirreps are given.",
    "arxiv_id": "q-alg/9701031",
    "authors": [
      "C. Quesne",
      "N. Vansteenkiste"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "doi": "10.1023/A:1021408531528",
    "journal_ref": "Czech. J. Phys. 47 (1997) 115-122",
    "title": "Representation Theory of Generalized Deformed Oscillator Algebras",
    "url": "https://arxiv.org/abs/q-alg/9701031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dc6340e6-7e07-4485-a3d6-f60c1ef267bd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}