NUI Galway Mathematics
Preprint IRL-GLWY-2006-001 (PDF)

AROUND SOLOMON'S DESCENT ALGEBRAS

C. Bonnafé and G. Pfeiffer

Abstract

We study different problems related to Solomon's descent algebra Σ(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 Σ(W) is equal to [(|S|+1)/2].

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