Coincidences between characters to hooks and 2-part partitions on families arising from 2-regular classes

TL;DR

This paper uncovers unexpected coincidences between characters of 2-part partitions and hooks in specific algebraic families, extending 2-regular conjugacy classes, refining previous results by Regev, Regev, and Zeilberger.

Contribution

It establishes new surprising character coincidences between 2-part partitions and hooks on extended 2-regular classes, refining prior algebraic results.

Findings

Identifies coincidences between characters of 2-part partitions and hooks.

Extends 2-regular conjugacy classes to reveal new character relationships.

Refines previous results by Regev, Regev, and Zeilberger.

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 hooks of size n+2 on two related families obtained by extending 2-regular conjugacy classes.