Angle-deformations in Coxeter groups

TL;DR

This paper simplifies the Coxeter group isomorphism problem by reducing it to identifying all sharp-angled Coxeter generating sets within the reflection set, streamlining the classification process.

Contribution

It introduces a reduction to determine Coxeter generating sets that are sharp-angled, advancing the understanding of Coxeter group structures.

Findings

Reduction to sharp-angled generating sets

Simplification of the isomorphism problem

Enhanced classification method for Coxeter groups

Abstract

The isomorphism problem for Coxeter groups has been reduced to its 'reflection preserving version' by B. Howlett and the second author. Thus, in order to solve it, it suffices to determine for a given Coxeter system (W,R) all Coxeter generating sets S of W which are contained in R^W, the set of reflections of (W,R). In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets S in R^W which are sharp-angled with respect to R.