Around Solomon's descent algebras

2006/01/13 by Bonnafé, Cédric, Pfeiffer, Götz
#05E99 (Secondary) #20F55 (Primary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0601317

Abstract

We study different problems related to the 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 \lceil |S| / 2 \rceil.

Related

• Cohomology of Coxeter arrangements and Solomon's descent algebra
• Properties of the Solomon homomorphism
• The Loewy length of the descent algebra of type D
• Generating series formulas for the structure constants of Solomon's descent algebra
• Computations for Coxeter arrangements and Solomon's descent algebra:\n Groups of rank three and four