The local recognition of reflection graphs of spherical Coxeter groups

TL;DR

This paper completes the local recognition of commuting reflection graphs associated with spherical Coxeter groups derived from irreducible crystallographic root systems, advancing understanding of their structural properties.

Contribution

It provides a complete local recognition framework for these reflection graphs, building on previous work and based on the third author's thesis.

Findings

Established local recognition criteria for reflection graphs

Extended previous classifications to irreducible crystallographic cases

Enhanced understanding of the structure of spherical Coxeter groups

Abstract

Based on the third author's thesis in this article we complete the local recognition of commuting reflection graphs of spherical Coxeter groups arising from irreducible crystallographic root systems.