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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 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 [(|S|+1)/2].

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