Intrinsic reflections in Coxeter systems

Abstract

Let $(W,S)$ be a Coxeter system and let $s\in S$. We call $s$ a right-angled generator of $(W,S)$ if $st=ts$ or $st$ has infinite order for each $t\in S$. We call $s$ an intrinsic reflection of $W$ if $s\in R^W$ for all Coxeter generating sets $R$ of $W$. We give necessary and sufficient conditions for a right-angled generator $s\in S$ of $(W,S)$ to be an intrinsic reflection of $W$.

References in corpus (5)

• Irreducible Coxeter groups
• The isomorphism problem for Coxeter groups
• Twist-rigid Coxeter groups
• Sur les automorphismes et la rigidite des groupes de Coxeter a angles droits
• Locally parabolic subgroups in Coxeter groups of arbitrary ranks

Cited by in corpus (1)

• A note on Weyl groups and crystallographic root lattices