A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements
Abstract
In this note, we provide a short and selfcontained 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2500
 Bibcode:
 2014arXiv1402.2500B
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 20F55
 EPrint:
 5 pages