Sign conjugacy classes of the symmetric groups

TL;DR

This paper classifies sign conjugacy classes in symmetric groups, confirming a conjecture of Olsson, and provides a comprehensive understanding of character values on these classes.

Contribution

It offers a complete classification of sign conjugacy classes in symmetric groups, resolving Olsson's conjecture.

Findings

Classification of all sign conjugacy classes in symmetric groups

Verification of Olsson's conjecture

Enhanced understanding of irreducible character values

Abstract

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.