Hurwitz equivalence of reflection factorizations in $G_7$

Abstract

We prove that two reflection factorizations of a given element in an exceptional rank-2 complex reflection group of tetrahedral type are Hurwitz-equivalent if and only if they generate the same subgroup and have the same multiset of conjugacy classes.

18 pages

Cited by in corpus (1)

• 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