Sylow branching coefficients and hook partitions

TL;DR

This paper characterizes how irreducible characters of symmetric groups, labeled by hook partitions, decompose when restricted to Sylow 2-subgroups, providing insights into their structure.

Contribution

It offers a detailed description of the irreducible constituents of symmetric group characters restricted to Sylow 2-subgroups, focusing on hook partitions.

Findings

Explicit description of irreducible constituents for hook partition characters

Enhanced understanding of Sylow 2-subgroup restrictions in symmetric groups

New combinatorial tools for analyzing character restrictions

Abstract

We give a description of the irreducible constituents of the restriction to Sylow 2-subgroups of irreducible characters of symmetric groups labelled by hook partitions.