The Capelli identity and Radon transform for Grassmannians

2015/11/16 by Siddhartha Sahi, Sahi, Siddhartha, Genkai Zhang +1
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Representation Theory (math.RT) #math.MG #math.RT

paper · pdf · doi:10.48550/arxiv.1511.04966

arxiv created 2015/11/16 · arxiv updated 2015/11/17

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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