Coincidences between Characters to Hook Partitions and 2-Part Partitions on Families arising from 2-Regular Classes

Abstract

Strongly refining results by Regev, Regev and Zeilberger, we prove surprising coincidences between characters to 2-part partitions of size $n$ and characters to hook partitions of size $n+2$ on two related families obtained by extending 2-regular conjugacy classes.