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Proceedings of the London Mathematical Society Advance Access published online on January 11, 2007
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdl015
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© 2007 London Mathematical Society

Reflection rigidity of 2-spherical Coxeter groups

Pierre-Emmanuel Caprace and Bernhard Mühlherr

Département de Mathématiques
Université libre de Bruxelles, CP216
Boulevard du Triomphe
B-1050 Bruxelles
Belgium
bmuhlherr{at}ulb.ac.be

Received 19 November 2003. Revision received 10 May 2006.

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.

Current address of P.-E. Caprace: Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford, OX1 3LB, United Kingdom, caprace@maths.ox.ac.uk


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