The Capelli Identity and Radon Transform for Grassmannians

Journal article, 2017

We study a family C-s,C-l of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The C-s,C-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,C-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.