Geodesic
Spectral properties of descent algebra elements.
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 127-139.

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

We determine the eigenvalues and their corresponding multiplicities of the action on the group algebra of a finite Coxeter group of an element of its descent algebra. Meanwhile, we identify a slight error in the paper of F. Bergeron, N. Bergeron, R. B. Howlett, and D. E. Taylor [J. Algebr. Comb. 1, No. 1, 23-44 (1992; Zbl 0798.20031)] in a formula for certain structure coefficients in the descent algebra. We provide the correct formula, and give an example which explicitly shows the difference between both formulas.
Classification : 20F55, 20C05, 05E10
Keywords: descent algebras, finite Coxeter groups, group algebras, regular representation, eigenvalues, multiplicities 
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Randriamaro, Hery. Spectral properties of descent algebra elements.. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 127-139. http://geodesic.mathdoc.fr/item/JAC_2014__39_1_a4/