{
  "id": "2412.01938",
  "version": "v1",
  "published": "2024-12-02T20:00:36.000Z",
  "updated": "2024-12-02T20:00:36.000Z",
  "title": "Eigenvalues of Heckman-Polychronakos operators",
  "authors": [
    "Charles Dunkl",
    "Vadim Gorin"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.CA",
    "math.CO",
    "math.MP"
  ],
  "abstract": "Heckman-Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators $\\mathcal D_i$ as $\\mathcal P_m= \\sum_{i=1}^N (x_i \\mathcal D_i)^m$. They have been known since 1990s in connection with trigonometric Calogero-Moser-Sutherland Hamiltonian and Jack symmetric polynomials. We explicitly compute the eigenvalues of these operators for symmetric and skew-symmetric eigenfunctions, as well as partial sums of eigenvalues for general polynomial eigenfunctions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-02T20:00:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenvalues",
      "heckman-polychronakos operators form",
      "general polynomial eigenfunctions",
      "jack symmetric polynomials",
      "trigonometric calogero-moser-sutherland hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}