Pinnacles for Complex Reflection Groups

Abstract

We study, characterize, and enumerate the admissible pinnacle sets of nonexceptional complex reflection groups $G(m,p,n)$, which include all generalized symmetric groups ${\mathbb{Z}}_m\wr S_n$ as special cases. This generalizes the work of Davis--Nelson--Petersen--Tenner for symmetric groups $S_n$ and González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for signed symmetric groups ${\mathbb{Z}}_2\wr S_n$. As a consequence, we prove a conjecture of González--Harris--Rojas Kirby--Smit Vega Garcia--Tenner for pinnacles of signed permutations.

20 pages, 2 figures