Reflection rigidity of 2-spherical Coxeter groups

We prove that each finitely generated, irreducible and 2-sphericalCoxeter system (W, S) is strongly reflection rigid wheneverthe group W is of infinite order. This means in particular thatall reflection-preserving automorphisms of such a group areinner-by-graph. Our result can be seen as a first major steptowards a proof of the conjecture that all infinite, irreducibleCoxeter systems are strongly reflection rigid if they do notadmit diagram twists.