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arXiv · 1512.04764

On the Hurwitz action in finite Coxeter groups

Barbara Baumeister·Thomas Gobet·Kieran Roberts·Patrick Wegener
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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.

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Barbara Baumeister, Thomas Gobet, Kieran Roberts, Patrick Wegener. 2015-12-15. On the Hurwitz action in finite Coxeter groups. https://arxiv.org/abs/1512.04764

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