On the Hurwitz action in finite Coxeter groups
Group Theory
2015-12-16 v1 Combinatorics
Abstract
We provide a necessary and sufficient condition on an element of a finite Coxeter group to ensure the transitivity of the Hurwitz action on its set of reduced decompositions into products of reflections. We show that this action is transitive if and only if the element is a parabolic quasi-Coxeter element, that is, if and only if it has a reduced decomposition into a product of reflections that generate a parabolic subgroup.
Keywords
Cite
@article{arxiv.1512.04764,
title = {On the Hurwitz action in finite Coxeter groups},
author = {Barbara Baumeister and Thomas Gobet and Kieran Roberts and Patrick Wegener},
journal= {arXiv preprint arXiv:1512.04764},
year = {2015}
}
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21 pages