A Note on the Transitive Hurwitz Action on Decompositions of Parabolic Coxeter Elements
نویسنده
چکیده
In this note, we provide a short and self-contained proof that the braid group on n strands acts transitively on the set of reduced factorizations of a Coxeter element in a Coxeter group of finite rank n into products of reflections. We moreover use the same argument to also show that all factorizations of an element in a parabolic subgroup of W also lie in this parabolic subgroup.
منابع مشابه
A Note on Parabolic Subgroups of a Coxeter Group
The aim of this note is to prove that the parabolic closure of any subset of a Coxeter group is a parabolic subgroup. To obtain that, several technical lemmas on the root system of a parabolic subgroup are established. MSC 2000 Subject Classifications: Primary 20F55; Secondary 20H15
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