Lattices of minimum covolume in Chevalley groups over local fields of positive characteristic

Abstract

In this article, we show that if $\mathbb{G}$ is a simply connected Chevalley group of either classical type of rank bigger than $1$ or type $E_6$ and if $q>9$ is a power of a prime number $p>5$, then $G=\mathbb{G}({\mathbb{F}}_q((t^{-1})))$, up to an automorphism, has a unique lattice of minimum covolume, which is $\mathbb{G}({\mathbb{F}}_q[t])$