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arXiv · 1511.04966

The Capelli identity and Radon transform for Grassmannians

Siddhartha Sahi·Genkai Zhang
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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.

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Siddhartha Sahi, Genkai Zhang. 2015-11-16. The Capelli identity and Radon transform for Grassmannians. https://arxiv.org/abs/1511.04966

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