Hurwitz Actions on Reflection Factorizations in Complex Reflection Group $G_6$

Abstract

We show that in the complex reflection group $G_6$, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.

14 pages

Cited by in corpus (2)

• Hurwitz equivalence of reflection factorizations in $G_7$
• In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants