Twist-rigid Coxeter groups

TL;DR

This paper proves that for certain finitely generated Coxeter groups, angle-compatible generating sets are conjugate if one set admits no elementary twist, advancing understanding of Coxeter group isomorphisms.

Contribution

It confirms a key case of a conjecture on Coxeter group isomorphisms by linking elementary twists to conjugacy of generating sets.

Findings

Two angle-compatible Coxeter generating sets are conjugate if one admits no elementary twist.

Supports a broader conjecture on Coxeter group isomorphism problem.

Advances classification of Coxeter groups based on generating set properties.

Abstract

We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which describes a potential solution to the isomorphism problem for Coxeter groups.