{
  "id": "1511.04966",
  "version": "v1",
  "published": "2015-11-16T14:17:46.000Z",
  "updated": "2015-11-16T14:17:46.000Z",
  "title": "The Capelli identity and Radon transform for Grassmannians",
  "authors": [
    "Siddhartha Sahi",
    "Genkai Zhang"
  ],
  "categories": [
    "math.RT",
    "math.MG"
  ],
  "abstract": "We study a family $C_{s,l}$ of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The $C_{s,l}$ descend to invariant differential operators on the corresponding Grassmannian, which is a compact symmetric space, and we determine the image of the $C_{s,l}$ under the Harish-Chandra homomorphism. We also obtain analogous results for corresponding operators on the non-compact duals of the Grassmannians, and for line bundles. As an application we obtain a Radon inversion formula, which generalizes a recent result of B. Rubin for real Grassmannians.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-16T14:17:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "radon transform",
      "capelli identity",
      "grassmannian",
      "capelli-type invariant differential operators",
      "radon inversion formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151104966S"
    }
  }
}