Around Solomon's descent algebras

Cédric Bonnafé (1) , Götz Pfeiffer (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 Department of Mathematics

We study different problems related to the Solomon's descent algebra $\Sigma(W)$ of a finite Coxeter group $(W,S)$: positive elements, morphisms between descent algebras, Loewy length... One of the main result is that, if $W$ is irreducible and if the longest element is central, then the Loewy length of $\Sigma(W)$ is equal to $\lceil |S| / 2 \rceil$.

Mots clés: Solomon's descent algebra; Loewy length

Domaines: Théorie des représentations [math.RT]

Cédric Bonnafé, Götz Pfeiffer. Around Solomon's descent algebras. 2008. ⟨hal-00016882v2⟩