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A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements

2014; American Mathematical Society; Volume: 1; Issue: 13 Linguagem: Inglês

10.1090/s2330-1511-2014-00017-1

2330-1511

Barbara Baumeister, Matthew Dyer, Christian Stump, Patrick Wegener,

Geometric and Algebraic Topology

In this note, we provide a short and self-contained proof that the braid group on n n strands acts transitively on the set of reduced factorizations of a Coxeter element in a Coxeter group of finite rank n 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 W also lie in this parabolic subgroup.