Angle-deformations in Coxeter groups

Abstract

The isomorphism problem for Coxeter groups has been reduced to its “reflection preserving version” by B Howlett and the second author. Thus, in order to solve it, it suffices to determine for a given Coxeter system $\left(W,R\right)$ all Coxeter generating sets $S$ of $W$ which are contained in $R^W$, the set of reflections of $\left(W,R\right)$. In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets $S\subseteq R^W$ which are sharp-angled with respect to $R$.

Added 22 May 2012: The description of Figure 3 in Section 8.1 has been corrected.