标题： Weyl群对Radon超几何函数及其对称性的作用 显示英文标题

标题： Weyl group action on Radon hypergeometric function and its symmetry

摘要： For positive integers $r,n,N:=rn$, we consider the Radon hypergeometric function (Radon HGF) associated with a partition $\lambda$ of $n$ defined on the Grassmannian $Gr(m,N)$ for $r<m<N$, which is obtained as the Radon transform of a character of the group $H_{\lambda}\subset G:=GL(N)$. We study its symmetry described by the Weyl group analogue $N_{G}(H_{\lambda})/H_{\lambda}$. 我们考虑高斯HGF的厄米特矩阵积分类似物及其合流族，这些被理解为在$Gr(2r,4r)$上的Radon HGF，对于$\lambda$的分拆$4$，我们应用对称性结果到这些特殊情况，并推导出一个类似于高斯类似物的变换公式，这被看作是经典高斯HGF的“Kummer的24个解”的一部分。 我们为Kummer的合流HGF类似物推导出类似的变换公式。 显示英文摘要

摘要： For positive integers $r,n,N:=rn$, we consider the Radon hypergeometric function (Radon HGF) associated with a partition $\lambda$ of $n$ defined on the Grassmannian $Gr(m,N)$ for $r<m<N$, which is obtained as the Radon transform of a character of the group $H_{\lambda}\subset G:=GL(N)$. We study its symmetry described by the Weyl group analogue $N_{G}(H_{\lambda})/H_{\lambda}$. We consider the Hermitian matrix integral analogue of the Gauss HGF and its confluent family, which are understood as the Radon HGF on $Gr(2r,4r)$ for partitions $\lambda$ of $4$, we apply the result of symmetry to these particular cases and derive a transformation formula for the Gauss analogue which is known as a part of "24 solutions of Kummer" for the classical Gauss HGF. We derive a similar transformation formula for the analogue Kummer's confluent HGF.