Mathieu Carette (Université Libre de Bruxelles): Strong reflection
rigidity in Coxeter groups
The isomorphism problem for Coxeter groups is the problem of
deciding whether two Coxeter diagrams define isomorphic
groups. The answer to that problem is still open. First, we
present a reduction of the general problem to its
reflection-preserving version. Then, as an approach to
solving this new problem, we give a sufficient condition for
Coxeter groups to be strongly reflection rigid: if the
condition is satified, then two Coxeter generating sets
defining the same set of reflections are conjugate to each
other, which is the strongest rigidity one could hope for.