The Capelli identity and Radon transform for Grassmannians
Representation Theory
2015-11-17 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1511.04966,
title = {The Capelli identity and Radon transform for Grassmannians},
author = {Siddhartha Sahi and Genkai Zhang},
journal= {arXiv preprint arXiv:1511.04966},
year = {2015}
}