Properties of the descent algebras of type $D$

TL;DR

This paper provides straightforward combinatorial descriptions of the radical and irreducible representations of the descent algebra for Coxeter groups of type D, enhancing understanding of its algebraic structure.

Contribution

It introduces new combinatorial methods to describe the radical and irreducible representations of the descent algebra of type D Coxeter groups.

Findings

Combinatorial descriptions of the radical

Descriptions of irreducible representations

Applicable over any field

Abstract

We establish simple combinatorial descriptions of the radical and irreducible representations specifically for the descent algebra of a Coxeter group of type $D$ over any field.