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arXiv · 2105.08104

The Hurwitz action in complex reflection groups

Joel Brewster Lewis·Jiayuan Wang
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Abstract

We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive and give a simple criterion to tell when two shortest reflection factorizations belong to the same Hurwitz orbit. We also characterize the quasi-Coxeter elements (those with a shortest reflection factorization that generates the whole group) in $G(m, p, n)$.

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Joel Brewster Lewis, Jiayuan Wang. 2021-05-17. The Hurwitz action in complex reflection groups. https://doi.org/10.5070/c62156884

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