Abstract
ABSTRACTLet G be a group of symmetries of a Coxeter system (W,S), and let f:W→GL(V) be the linear representation associated with a root basis (V,⟨.,.⟩,Π). We show that WG is a Coxeter group, we construct a subset so that is a root basis of WG, and we show that the induced representation is the linear representation associated with . In particular, the latter is faithful.
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