On Radon hypergeometric functions on the Grassmannian manifold

2025/07/25 by Hironobu Kimura, Kimura, Hironobu · 2 citations
Mathematics · #33C70 #33C80 #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2507.19048

openalex publication_date 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a definition of Radon hypergeometric function (Radon HGF) of confluent and nonconfluent type, which is a function on the Grassmannian Gr(m,nr) obtained as a Radon transform of a character of the universal covering group of H_λ⊂ GL(nr) specified by a partition λof n, where H_(1,…,1)≃(GL(r))ⁿ. When r=1, the Radon HGF reduces to the Gelfand HGF on the Grassmannian. We give a system of differential equations satisfied by the Radon HGF and show that the Hermitian matrix integral analogues of Gauss HGF and its confluent family: Kummer, Bessel, Hermite-Weber and Airy function, are obtained in a unified manner as the Radon HGF on Gr(2r,4r) corresponding to the partitions (1,1,1,1), (2,1,1), (2,2), (3,1) and (4), respectively.

Citations

• Lectures on the geometry of flag varieties
• Stratifications de Whitney et théorème de Bertini-Sard

Cited by

• Weyl group action on Radon hypergeometric function and its symmetry
• Capelli identity and contiguity relations of Radon hypergeometric function on the Grassmannian

Related

• Capelli identity and contiguity relations of Radon hypergeometric function on the Grassmannian
• Weyl group action on Radon hypergeometric function and its symmetry
• Radon transform on real, complex and quaternionic Grassmannians
• Laplacian operators and Radon transforms on Grassmann graphs
• Radon, cosine and sine transforms on Grassmannian manifolds