Stable reflection length in Coxeter groups
Group Theory
2025-04-02 v1
Abstract
We introduce stable reflection length in Coxeter groups, as a way to study the asymptotic behaviour of reflection length. This creates connections to other well-studied stable length functions in groups, namely stable commutator length and stable torsion length. As an application, we give a complete characterisation of elements whose reflection length is unbounded on powers.
Cite
@article{arxiv.2504.00229,
title = {Stable reflection length in Coxeter groups},
author = {Francesco Fournier-Facio and Marco Lotz and Timothée Marquis},
journal= {arXiv preprint arXiv:2504.00229},
year = {2025}
}
Comments
12 pages