A NEW CLASS OF RIGID COXETER GROUPS

Abstract

A Coxeter group is said to be rigid if any two systems for that group yield isomorphic Coxeter diagrams. A Coxeter group is said to be strongly rigid if moreover the generating sets of any two systems are conjugate. We determine a new class of Coxeter groups which are rigid, and introduce the notion of reflection independence, a generalization of strong rigidity.