Around solomon’s descent algebras
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Bonnafé, C. Pfeiffer, G. (2008). Around solomon’s descent algebras. Algebras and Representation Theory 11 (6), 577-602
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 s/2.