Non-linear Sylow branching coefficients for symmetric groups

TL;DR

This paper investigates how irreducible characters of symmetric groups behave when restricted to Sylow subgroups, extending previous results to a broader context and focusing on constituents of higher degree.

Contribution

It provides a significant generalization of prior work on Sylow restrictions of symmetric group characters, especially for constituents of degree greater than one.

Findings

Extended the understanding of Sylow restriction behavior for symmetric groups

Generalized Theorem 3.1 of Giannelli and Navarro

Identified new properties of irreducible character constituents

Abstract

We study the restriction to Sylow subgroups of irreducible characters of symmetric groups. In particular, we focus our attention on constituents of degree greater than 1. Our main result is a wide generalization of Theorem 3.1 of Giannelli and Navarro, "Restricting irreducible characters to Sylow p-subgroups".