Around Solomon's descent algebras

Details Around Solomon's descent algebras Around Solomon's descent algebras

2006-01-13

arxiv.org/abs/math/0601317v2

Mathematics

Representation Theory

21 pages

Scientific paper

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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