Gelfand Pairs Obtained from the Finite Upper Half Planes over $\mathbb{Z}/2^n\mathbb{Z}$

Abstract

The general linear group $G$ over $\mathbb{Z}/2^n\mathbb{Z}$ acts transitively on the finite upper half plane over $\mathbb{Z}/2^n\mathbb{Z}$, where $\mathbb{Z}$ denotes the ring of rational integers. In this paper, it is shown that the pair of $G$ and the stabilizer of a point on the plane is a Gelfand pair.