Radon transform for $G{L}_n({\mathbb{F}}_q)$

Abstract

In this paper, we study the Radon transform associated with the unipotent radical subgroups of $G{L}_n({\mathbb{F}}_q)$. We analyze properties of the Radon transform with a specific emphasis on its eigenvalues. We provide a description of its eigenvalues for the cases of $G{L}_2({\mathbb{F}}_q)$ and $G{L}_3({\mathbb{F}}_q)$.