The capelli identity and radon transform for grassmannians

Siddhartha Sahi, Genkai Zhang

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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.

Original languageEnglish (US)
Pages (from-to)3774-3800
Number of pages27
JournalInternational Mathematics Research Notices
Issue number12
StatePublished - Jun 1 2017


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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