Geodesic
A decomposition of the descent algebra of a finite Coxeter group
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 23-44.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The purpose of this paper is twofold. First we aim to unify previous work by the first two authors, A. Garsia, and C. Reutenauer (see [2], [3], [4], [5] and [10]) on the structure of the descent algebras of the Coxeter groups of type $A _{n}$ and $B _{n}$. But we shall also extend these results to the descent algebra of an arbitrary finite Coxeter group $W.$ The descent algebra, introduced by Solomon in [14], is a subalgebra of the group algebra of $W$. It is closely related to the subring of the Burnside ring $B( W)$ spanned by the permutation representations $W/W _{J}$, where the $W _{J}$ are the parabolic subgroups of $W$. Specifically, our purpose is to lift a basis of primitive idempotents of the parabolic Burnside algebra to a basis of idempotents of the descent algebra.
Keywords: Coxeter groups, idempotents, descent algebra 
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     title = {A decomposition of the descent algebra of a finite {Coxeter} group},
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Bergeron, F.; Bergeron, N.; Howlett, R.B.; Taylor, D.E. A decomposition of the descent algebra of a finite Coxeter group. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 23-44. http://geodesic.mathdoc.fr/item/JAC_1992__1_1_a3/