On Radon hypergeometric functions on the Grassmannian manifold
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916863566413824 |
|---|---|
| author | Kimura, Hironobu |
| author_facet | Kimura, Hironobu |
| contents | 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\subset GL(nr) specified by a partition λof n, where H_{(1,\dots,1)}\simeq(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Radon hypergeometric functions on the Grassmannian manifold Kimura, Hironobu Classical Analysis and ODEs 33C70, 33C80 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\subset GL(nr) specified by a partition λof n, where H_{(1,\dots,1)}\simeq(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. |
| title | On Radon hypergeometric functions on the Grassmannian manifold |
| topic | Classical Analysis and ODEs 33C70, 33C80 |
| url | https://arxiv.org/abs/2507.19048 |