On the Hurwitz action in affine Coxeter groups
Group Theory
2019-09-27 v2 Combinatorics
Abstract
We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced factorizations into a product of reflections is transitive. We call an element of the Coxeter group parabolic quasi-Coxeter element if it has a reduced factorization into a product of reflections that generate a parabolic subgroup.
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Cite
@article{arxiv.1710.06694,
title = {On the Hurwitz action in affine Coxeter groups},
author = {Patrick Wegener},
journal= {arXiv preprint arXiv:1710.06694},
year = {2019}
}
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21 pages