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

In this article, we show that if 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 = G ( F q ( ( t − 1 ) ) ) , up to an automorphism, has a unique lattice of minimum covolume, which is G (...

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Bibliographic Details
Published in:Duke mathematical journal 2009-02, Vol.146 (2), p.227-251
Main Author: Golsefidy, Alireza Salehi
Format: Article
Language:English
Subjects:
11E57
20Gxx
22E40
32Nxx
Classical groups [See also 14Lxx
Discrete subgroups of Lie groups [See also 20Hxx
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Summary:In this article, we show that if 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 = G ( F q ( ( t − 1 ) ) ) , up to an automorphism, has a unique lattice of minimum covolume, which is G ( F q [ t ] )
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2008-064