Commensurability growths of algebraic groups

2018/09/27 by Bou-Rabee, Khalid, Kaletha, Tasho, Studenmund, Daniel
#20E26 #20G05 #20G20 #20G25 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1809.10332

Abstract

Fixing a subgroup Γ in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups Δ of G with [Γ: Γ∩ Δ][Δ: Γ∩ Δ] ≤ n. For pairs Γ≤ G, where G is a Chevalley group scheme defined over ℤ and Γ is an arithmetic lattice in G, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on G.

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