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Around Solomon's descent algebras

Cédric Bonnafé·Götz Pfeiffer
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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 $\lceil |S| / 2 \rceil$.

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Cédric Bonnafé, Götz Pfeiffer. 2008-05-30. Around Solomon's descent algebras. https://arxiv.org/abs/math/0601317

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