Stable reflection length in Coxeter groups

2025/03/31 by Francesco Fournier-Facio, Fournier-Facio, Francesco, Marco Lotz +3
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2504.00229

openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Bounding reflection length in an affine Coxeter group
• Powers of Coxeter elements with unbounded reflection length
• Stable Torsion Length
• Minimal length elements in some double cosets of Coxeter groups
• A refined count of Coxeter element factorizations