Sylow branching coefficients for symmetric groups

TL;DR

This paper introduces Sylow branching coefficients for symmetric groups by analyzing the irreducible constituents of induced characters from linear characters of Sylow p-subgroups, generalizing previous results.

Contribution

It provides a comprehensive description of irreducible constituents of induced characters from Sylow p-subgroups in symmetric groups, extending earlier work.

Findings

Explicit description of irreducible constituents

Introduction of Sylow branching coefficients

Generalization of previous results

Abstract

Let $p\ge 5$ be a prime and let $n$ be a natural number. In this article we describe the irreducible constituents of the induced characters $\phi\big\uparrow^{\mathfrak{S}_n}$ for arbitrary linear characters $\phi$ of a Sylow $p$-subgroup of the symmetric group $\mathfrak{S}_n$, generalising earlier results of the authors. By doing so, we introduce Sylow branching coefficients for symmetric groups.