A step towards Twist Conjecture

TL;DR

This paper proves Mühllherr's Twist Conjecture for Coxeter groups with defining graphs that admit only $Z_2$ twists and are of type FC, advancing understanding of Coxeter group symmetries.

Contribution

It establishes the Twist Conjecture under specific conditions on the Coxeter group's defining graph, a novel result in the theory of Coxeter groups.

Findings

Proves Mühllherr's Twist Conjecture for certain Coxeter groups.

Identifies conditions on defining graphs that guarantee the conjecture.

Advances the theoretical understanding of Coxeter group automorphisms.

Abstract

Under the assumption that a defining graph of a Coxeter group admits only twists in $\mathbb{Z}_2$ and is of type FC, we prove M\"uhlherr's Twist Conjecture.