A decomposition of the descent algebra of a finite Coxeter group
type: Item
instance of: scholarly article
title: A decomposition of the descent algebra of a finite Coxeter group
zbMATH Open document ID: 0798.20031
DOI: 10.1023/A:1022481230120
author: Juan-Miguel Gracia
published in: Journal of Algebraic Combinatorics
publication date: 1993-11-01T00:00:00Z
review text: 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.
reviewed by: Christophe Reutenauer
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 19A22
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 427648
zbMATH Keywords: primitive idempotents
zbMATH Keywords: descent algebra
zbMATH Keywords: symmetric groups
zbMATH Keywords: hyperoctahedral groups
zbMATH Keywords: finite Coxeter groups
zbMATH Keywords: parabolic Burnside algebras
zbMATH Keywords: representations
zbMATH Keywords: radical
MaRDI profile type: Publication
cites work: Q3722697
cites work: A decomposition of the descent algebra of the hyperoctahedral group. I, II
cites work: Symbolic manipulation for the study of the descent algebra of finite Coxeter groups
cites work: Homomorphisms between Solomon's descent algebras
cites work: Q3941610
cites work: Q3682663
cites work: Q5668957
cites work: Q3491770
cites work: A decomposition of Solomon's descent algebra
cites work: Normalizers of Parabolic Subgroups of Reflection Groups
cites work: Finite Unitary Reflection Groups
cites work: Invariants of Finite Reflection Groups
cites work: A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
cites work: Endomorphisms of linear algebraic groups
full work available at URL: a:1022481230120
OpenAlex ID: W1524416588
description: scientific article; zbMATH DE number 427648