Reflection rigidity of 2-spherical Coxeter groups

We prove that each finitely generated, irreducible and 2-spherical Coxeter system (W, S) is strongly reflection rigid whenever the group W is of infinite order. This means in particular that all reflection-preserving automorphisms of such a group are inner-by-graph. Our result can be seen as a first major step towards a proof of the conjecture that all infinite, irreducible Coxeter systems are strongly reflection rigid if they do not admit diagram twists