Invariant random subgroups in hyperbolic reflection groups
Group Theory
2026-01-06 v1
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.
Cite
@article{arxiv.2601.02195,
title = {Invariant random subgroups in hyperbolic reflection groups},
author = {Jean Raimbault},
journal= {arXiv preprint arXiv:2601.02195},
year = {2026}
}