{
  "annotation_id": "7be7673c-dc35-46a5-a626-06f2366a5932",
  "date_created": "2026-03-02T18:01:17.821000Z",
  "date_modified": "2026-03-02T18:01:17.821000Z",
  "file_hash": "8fea7a552b009c0c8432f708059231038290eb936071fed9fa1abdbed0b8486d",
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  "record": {
    "abstract": "A full set of (higher order) Casimir invariants for the Lie algebra\n$gl(\\infty )$ is constructed and shown to be well defined in the category\n$O_{FS}$ generated by the highest weight (unitarizable) irreducible\nrepresentations with only a finite number of non-zero weight components.\nMoreover the eigenvalues of these Casimir invariants are determined explicitly\nin terms of the highest weight. Characteristic identities satisfied by certain\n(infinite) matrices with entries from $gl(\\infty )$ are also determined and\ngeneralize those previously obtained for $gl(n)$ by Bracken and Green.$^{1,2}$",
    "arxiv_id": "physics/9612009",
    "authors": [
      "M. D. Gould",
      "N. I. Stoilova"
    ],
    "categories": [
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.532123",
    "journal_ref": "J.Math.Phys. 38 (1997) 4783-4793",
    "title": "Casimir invariants and characteristic identities for $gl(\\infty )$",
    "url": "https://arxiv.org/abs/physics/9612009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "826fc773-45ce-42af-8cbd-5e845619ee7d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}