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Preprints, Working Papers, ... Year : 2006

Around Solomon's descent algebras

Götz Pfeiffer
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Abstract

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 $\lceil |S| / 2 \rceil$.
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Dates and versions

hal-00016882 , version 1 (13-01-2006)
hal-00016882 , version 2 (30-05-2008)

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Cédric Bonnafé, Götz Pfeiffer. Around Solomon's descent algebras. 2006. ⟨hal-00016882v1⟩
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