{
  "id": "physics/9612009",
  "version": "v1",
  "published": "1996-12-12T05:58:21.000Z",
  "updated": "1996-12-12T05:58:21.000Z",
  "title": "Casimir invariants and characteristic identities for $gl(\\infty )$",
  "authors": [
    "M. D. Gould",
    "N. I. Stoilova"
  ],
  "comment": "10 pages, PlainTex",
  "journal": "J.Math.Phys. 38 (1997) 4783-4793",
  "doi": "10.1063/1.532123",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A full set of (higher order) Casimir invariants for the Lie algebra $gl(\\infty )$ is constructed and shown to be well defined in the category $O_{FS}$ generated by the highest weight (unitarizable) irreducible representations with only a finite number of non-zero weight components. Moreover the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from $gl(\\infty )$ are also determined and generalize those previously obtained for $gl(n)$ by Bracken and Green.$^{1,2}$",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-12-12T05:58:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "casimir invariants",
      "characteristic identities",
      "highest weight",
      "non-zero weight components",
      "lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 1997,
      "month": "Sep",
      "volume": 38,
      "number": 9,
      "pages": 4783
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 427699,
      "adsabs": "1997JMP....38.4783G"
    }
  }
}