Simply laced Coxeter groups and groups generated by symplectic transvections.
Simply laced Coxeter groups and groups generated by symplectic transvections.
Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u,v) in the Coxeter group W\times W. We associate to i a subgroup Gamma_i in …