A decomposition of the descent algebra of a finite Coxeter group
This paper unifies previous work of A. Garcia and the reviewer, and of the two first authors, which gave the primitive idempotents of the descent algebra of the symmetric group and of the hyperoctahedral group [Adv. Math. 77, No. 2, 189-262 (1989; Zbl 0716.20006), J. Algebra 148, 86-97 and 98-122 (1992; Zbl 0798.20008)]. These idempotents are constructed in a uniform way for each finite Coxeter group \(W\). They are lifted from the parabolic Burnside algebra. The dimensions of the corresponding representations of \(W\) are given, the radical of the descent algebra is determined and the link with the exponents of \(W\) is given.
scientific article; zbMATH DE number 427648
scientific article