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arXiv · 1402.2500

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

Barbara Baumeister·Matthew Dyer·Christian Stump·Patrick Wegener
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Abstract

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 lie as well in this parabolic subgroup.

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Barbara Baumeister, Matthew Dyer, Christian Stump, Patrick Wegener. 2014-02-11. A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements. https://arxiv.org/abs/1402.2500

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