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The Hurwitz action in complex reflection groups

  • Author(s): Lewis, Joel Brewster;
  • Wang, Jiayuan
  • et al.

Published Web Location Commons 'BY' version 4.0 license

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 $G(m, p, n)$.

Mathematics Subject Classifications: 05A05, 05A15, 05E18, 20F55

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