Rigidity of Coxeter groups and Artin groups (Q1855282)

A Coxeter group is called rigid if it cannot be defined by two nonisomorphic diagrams. The authors show that an example of a nonrigid Coxeter group belongs to a ``diagram twisting operation'' and that Coxeter groups, belonging to twisted diagrams, are isomorphic. A Coxeter system \((W,S)\) is called reflection rigid, if every Coxeter generating set \(S'\) contained in the set of reflections \(R_S\) determines the same diagram as \((W,S)\). The authors give a number of Coxeter groups which are reflection rigid once twisting is taken into account.