{
  "id": "1011.0151",
  "version": "v1",
  "published": "2010-10-31T12:40:15.000Z",
  "updated": "2010-10-31T12:40:15.000Z",
  "title": "On duality and negative dimensions in the theory of Lie groups and symmetric spaces",
  "authors": [
    "Ruben L. Mkrtchyan",
    "Alexander P. Veselov"
  ],
  "comment": "11 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show also that such relations can be extended to the classical symmetric spaces using Macdonald duality for Jack and Jacobi symmetric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-31T12:40:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "53C35",
      "11.30.Ly",
      "02.20.Qs"
    ],
    "keywords": [
      "lie groups",
      "negative dimensions",
      "jacobi symmetric functions",
      "casimir operators",
      "symbolic formulae"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3625954",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Aug",
      "volume": 52,
      "number": 8,
      "pages": 3514
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 875316,
      "adsabs": "2011JMP....52h3514M"
    }
  }
}