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.


S. Sahi

Genkai Zhang

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

12 3774-3800

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