On the complexities of some simple modules of symmetric groups

TL;DR

This paper investigates the complexities of certain simple modules of symmetric groups labeled by two-part partitions, especially those in blocks with non-abelian defect groups, providing new insights into their structural properties.

Contribution

It computes complexities of simple modules in symmetric groups associated with two-part partitions, focusing on those in non-abelian defect blocks, advancing understanding of modular representation theory.

Findings

Computed complexities for simple modules labeled by two-part partitions

Identified complexities within blocks with non-abelian defect groups

Enhanced understanding of module structures in symmetric groups

Abstract

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect groups.