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Reflection rigidity of 2-spherical Coxeter groups

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Caprace, Pierre-Emmanuel [UCL] Mühlherr, Bernhard [UCL]

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.

Document type Article de périodique (Journal article)
Publication date 2007
Language Anglais
Journal information "Proceedings of the London Mathematical Society" - Vol. 94, no. 2, p. 520-542 (2007)
Peer reviewed yes
Publisher London Mathematical Society
issn 0024-6115
e-issn 1460-244X
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
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Bibliographic reference Caprace, Pierre-Emmanuel ; Mühlherr, Bernhard. Reflection rigidity of 2-spherical Coxeter groups. In: Proceedings of the London Mathematical Society, Vol. 94, no. 2, p. 520-542 (2007)
Permanent URL http://hdl.handle.net/2078.1/94575