Reflection rigidity of 2-spherical Coxeter groups

Caprace, Pierre-Emmanuel;Mühlherr, Bernhard
(2007) Proceedings of the London Mathematical Society — Vol. 94, n° 2, p. 520-542 (2007)

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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.
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Caprace, P.-E., & Mühlherr, B. (2007). Reflection rigidity of 2-spherical Coxeter groups. Proceedings of the London Mathematical Society, 94(2), 520-542. https://doi.org/10.1112/plms/pdl015 (Original work published 2007)