The Capelli identity and Radon transform for Grassmannians
arXiv:1511.04966
Abstract
We study a family of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The descend to invariant differential operators on the corresponding Grassmannian, which is a compact symmetric space, and we determine the image of the 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.