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Proceedings of the London Mathematical Society Advance Access originally published online on January 11, 2007
Proceedings of the London Mathematical Society 2007 94(2):520-542; 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{at}maths.ox.ac.uk


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