{
  "id": "math-ph/0101028",
  "version": "v1",
  "published": "2001-01-25T09:21:58.000Z",
  "updated": "2001-01-25T09:21:58.000Z",
  "title": "Darboux Coordinates on K-Orbits and the Spectra of Casimir Operators on Lie Groups",
  "authors": [
    "I. V. Shirokov"
  ],
  "comment": "LaTeX2e, 15pp, no figures",
  "journal": "Theoretical and Mathematical Physics, Vol. 123, No. 3, 2000",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We propose an algorithm for obtaining the spectra of Casimir (Laplace) operators on Lie groups. We prove that the existence of the normal polarization associated with a linear functional on the Lie algebra is necessary and sufficient for the transition to local canonical Darboux coordinates $(p,q)$ on the coadjoint representation orbit that is linear in the \"momenta.\" We show that the $\\la$-representations of Lie algebras (which are used, in particular, in integrating differential equations) result from the quantization of the Poisson bracket on the coalgebra in canonical coordinates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-25T09:21:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie groups",
      "casimir operators",
      "lie algebra",
      "local canonical darboux coordinates",
      "coadjoint representation orbit"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.ph...1028S"
    }
  }
}