Strong rigidity in even Coxeter groups
by
Patrick Bahls
University of Illinois, Urbana-Champaign

A Coxeter group W is said to be strongly rigid if any two fundamental generating sets for W are conjugate to one another. We characterize all strongly rigid even Coxeter groups with Coxeter diagram V of one of the following forms:

1.  V has no edges labeled 2,

2.  V has no simple cycles of length less than 5.

Furthermore, we indicate how the method of proof can be used to compute Aut(W) for certain Coxeter groups W, and to show rigidity and strong rigidity of other classes of Coxeter groups.

Date received: February 26, 2003