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February 2012 Counting lattices in simple Lie groups: The positive characteristic case
Alireza Salehi Golsefidy
Duke Math. J. 161(3): 431-481 (February 2012). DOI: 10.1215/00127094-1507421

Abstract

In this article, we prove the following conjecture by Lubotzky. Let G=G0(K), where K is a local field of characteristic p5 and where G0 is a simply connected, absolutely almost simple K-group of K-rank at least 2. We give the rate of growth of

ρx(G ):=|{ΓG|Γ a lattice in G,vol(G/Γ)x}/|,

where Γ1Γ2 if and only if there is an abstract automorphism θ of G such that Γ2=θ(Γ1). We also study the rate of subgroup growth sx(Γ) of any lattice Γ in G. As a result, we show that these two functions have the same rate of growth, which proves Lubotzky’s conjecture. Along the way, we also study the rate of growth of the number of equivalence classes of maximal lattices in G with covolume at most x.

Citation

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Alireza Salehi Golsefidy. "Counting lattices in simple Lie groups: The positive characteristic case." Duke Math. J. 161 (3) 431 - 481, February 2012. https://doi.org/10.1215/00127094-1507421

Information

Published: February 2012
First available in Project Euclid: 1 February 2012

zbMATH: 1243.22011
MathSciNet: MR2881228
Digital Object Identifier: 10.1215/00127094-1507421

Subjects:
Primary: 22E40
Secondary: 20E07

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 3 • February 2012
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