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arXiv · 2511.06996

The limit cone and bounds on the growth indicator function

Lasse Lennart Wolf
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Abstract

Given a real semisimple Lie group $G$ with finite center and a discrete subgroup $Γ\subset G$ whose limit cone is disjoint from two facets of the Weyl chamber we show that Quint's growth indicator function $ψ_Γ$ is bounded by the half sum of positive roots $ρ$, i.e. it has slow growth, implying that the representation $L^2(Γ\backslash G)$ is tempered. In particular, this holds for each $I$-Anosov subgroup provided that $I$ contains at least two distinct simple roots that are not interchanged by the opposition involution.

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Lasse Lennart Wolf. 2026-08-03. The limit cone and bounds on the growth indicator function. https://arxiv.org/abs/2511.06996

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