The Picky and Subnormalizer Conjectures for symmetric groups

TL;DR

This paper explores new conjectures related to characters of symmetric groups, extending ideas connected to the McKay conjecture, and investigates their validity within the context of finite symmetric groups.

Contribution

It introduces and studies new character conjectures for symmetric groups, expanding the theoretical framework related to the McKay conjecture.

Findings

Proposes new conjectures for symmetric groups' characters

Provides evidence supporting these conjectures in specific cases

Connects the conjectures to existing theories like the McKay conjecture

Abstract

A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.