Around Solomon's descent algebras
Cédric Bonnafé, Götz Pfeiffer
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 |S| / 2 .
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