A note on the Hurwitz action on reflection factorizations of Coxeter elements in complex reflection groups

Abstract

We show that the Hurwitz action is "as transitive as possible" on reflection factorizations of Coxeter elements in the well-generated complex reflection groups $G(d,1,n)$ (the group of $d$-colored permutations) and $G(d,d,n)$.

arXiv comment11 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