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arXiv · 2601.02195

Invariant random subgroups in hyperbolic reflection groups

Jean Raimbault
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Abstract

We prove that the Fuchsian (4,4,4) triangle group and also right-angled reflection groups of hyperbolic spaces in higher dimensions admit ergodic invariant random subgroups having uncountably many isomorphism types of subgroups in their support (in most cases we actually prove a stronger statement), providing an answer to a question of S. Thomas. We also give similar constructions in higher-dimensional spaces. Our constructions are based on Coxeter polytopes in hyperbolic spaces. We also provide examples of invariant random subgroups related to questions of Y. Glasner and A. Hase through a similar construction.

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Jean Raimbault. 2026-01-05. Invariant random subgroups in hyperbolic reflection groups. https://arxiv.org/abs/2601.02195

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