The Capelli identity and Radon transform for Grassmannians

الأصل · EN

We study a family Cₛ,ₗ of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The Cₛ,ₗ descend to invariant differential operators on the corresponding Grassmannian, which is a compact symmetric space, and we determine the image of the Cₛ,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.