Sign conjugacy classes of the alternating groups

TL;DR

This paper classifies sign conjugacy classes in alternating groups, where each class's irreducible characters only take values 0, 1, or -1, enhancing understanding of their character theory.

Contribution

It provides a complete classification of sign conjugacy classes specifically for alternating groups, a problem not previously fully resolved.

Findings

Complete classification of sign conjugacy classes in alternating groups

Characterization of classes with restricted character values

Advancement in understanding the representation theory of alternating groups

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 alternating groups.