Coxeter groups and automorphisms

Abstract

Let $(W,S)$ be a Coxeter system and $\Gamma$ be a group of automorphisms of $W$ such that $\gamma (S)=S$ for all $\gamma \in \Gamma$. Then it is known that the group of fixed points $W^{\Gamma }$ is again a Coxeter group with a canonically defined set of generators. The usual proofs of this fact rely on the reflection representation of $W$. Here, we give a proof which only uses the combinatorics of reduced expressions in $W$. As a by-product, this shows that the length function on $W$ restricts to a weight function on $W^{\Gamma }$.

4 pages

Cited by in corpus (1)

• On Extending Unipotent Representations to their Stabilizers