The p-modular Descent Algebra of the Symmetric Group

TL;DR

This paper investigates the structure of the p-modular descent algebra of the symmetric group, defining a homomorphism to analyze its radical, nilpotency, and irreducible representations in characteristic p.

Contribution

It introduces a homomorphism into the algebra of p-modular characters to determine the radical, nilpotency index, and irreducible representations of the descent algebra.

Findings

Determined the radical and its nilpotency index.

Described the irreducible representations of the descent algebra.

Established a homomorphism into the algebra of p-modular characters.

Abstract

The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the radical, and its nilpotency index. It also allows the irreducible representations of the descent algebra to be described.