Coxeter groups as Beauville groups

TL;DR

This paper classifies Coxeter groups that are Beauville groups, extending previous work, and shows that none are mixed Beauville groups or mixable, providing a comprehensive understanding of their Beauville properties.

Contribution

It generalizes prior classifications to all Coxeter groups, identifying which are strongly real Beauville groups and which are Beauville groups, and rules out mixed Beauville structures.

Findings

Identifies which Coxeter groups are strongly real Beauville groups

Determines which Coxeter groups are Beauville groups

Proves no Coxeter group is a mixed Beauville group or mixable

Abstract

We generalize earlier work of Fuertes and Gonz\'{a}lez-Diez as well as earlier work of Bauer, Catanese and Grunewald to Coxeter groups in general by classifying which of these are strongly real Beauville groups. As a consequence of this we determine which of these groups are Beauville groups. We also show that none of these groups are mixed Beaville groups as well as proving that no Coxeter group is a mixable Beauville group.