Around Solomon's descent algebras
classification
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descentalgebraslengthloewysigmasolomonalgebraaround
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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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