C. Bonnafé and G. Pfeiffer,
# Around Solomon's descent algebras.

*Algebr. Represent. Theory* (2008), 26 pages.
DOI 10.1007/s10468-008-9090-9.
Preprint IRL-GLWY-2006-001.
arXiv:math.RT/0601317.

## Abstract.

We study different problems related to 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
$[(|S|+1)/2]$.
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