Vertices of simple modules of symmetric groups labelled by hook partitions

TL;DR

This paper classifies the vertices of simple modules of symmetric groups labeled by hook partitions in prime characteristic, completing the understanding of their structure.

Contribution

It provides a complete classification of vertices for simple modules labeled by hook partitions, advancing the representation theory of symmetric groups.

Findings

Complete classification of vertices for hook-labeled simple modules

Enhanced understanding of module structure in prime characteristic

Clarification of the relationship between partitions and module vertices

Abstract

In this article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions.