Dihedral twists in the Twist Conjecture

TL;DR

This paper proves Bernhard Mühlherr's Twist Conjecture for Coxeter groups under specific conditions on their defining graphs, involving elementary twists and the FC type, advancing understanding of Coxeter group automorphisms.

Contribution

The paper establishes the Twist Conjecture for a class of Coxeter groups with graphs admitting only elementary twists of certain types and being of FC type, a significant step in Coxeter group theory.

Findings

Proves the Twist Conjecture under specified graph conditions

Shows that certain Coxeter groups satisfy the conjecture

Advances the classification of Coxeter group automorphisms

Abstract

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