Symmetric generation of Coxeter groups

TL;DR

This paper introduces a method for generating Coxeter groups using involutory symmetric sets, applicable to finite, affine, and hyperbolic cases, offering a new perspective on their structure.

Contribution

It presents a novel symmetric generation approach for Coxeter groups that broadens understanding of their algebraic structure under specific finiteness conditions.

Findings

Applicable to finite, affine, and hyperbolic Coxeter groups

Provides involutory symmetric generating sets

Fulfills a specific finiteness condition

Abstract

We provide involutory symmetric generating sets of finitely generated Coxeter groups, fulfilling a suitable finiteness condition, which in particular is fulfilled in the finite, affine and compact hyperbolic cases.