English

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.

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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}
}

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12 pages