Lattices of minimum covolume in Chevalley groups over local fields of positive characteristic
Alireza Salehi Golsefidy
Source: Duke Math. J. Volume 146, Number 2
(2009), 227-251.
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 ${\rm E}_6$ and if $q>9$ is a power of a prime number $p>5$, then $G=\mathbb{G}\big(\mathbb{F}_q((t^{-1}))\big)$, up to an automorphism, has a unique lattice of minimum covolume, which is $\mathbb{G}(\mathbb{F}_q[t])$
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1231170939
Digital Object Identifier: doi:10.1215/00127094-2008-064
Mathematical Reviews number (MathSciNet): MR2477760
Zentralblatt MATH identifier: 1161.22006
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