Reflection rigidity of 2-spherical Coxeter groups |
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Authors: | Caprace, Pierre-Emmanuel Muhlherr, Bernhard |
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Affiliation: | Département de Mathématiques Université libre de Bruxelles CP216 Boulevard du Triomphe B-1050 Bruxelles Belgium bmuhlherr{at}ulb.ac.be |
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Abstract: | 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. |
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