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Reflection rigidity of 2‐spherical Coxeter groups
Author(s) -
Caprace PierreEmmanuel,
Mühlherr Bernhard
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl015
Subject(s) - coxeter group , mathematics , point group , reflection (computer programming) , rigidity (electromagnetism) , artin group , longest element of a coxeter group , coxeter complex , coxeter graph , coxeter element , pure mathematics , conjecture , combinatorics , reflection group , graph , physics , computer science , programming language , voltage graph , quantum mechanics , line graph
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.