Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups. With an appendix by Pierre Baumann and Christophe Hohlweg.
type: Item
instance of: scholarly article
title: Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups. With an appendix by Pierre Baumann and Christophe Hohlweg.
zbMATH Open document ID: 1098.20011
author: Cédric Bonnafé
author: Christophe Hohlweg
publication date: 2006-03-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10137
review text: This article is written neatly in a very clear way. It develops some results on Weyl groups and its consequences. After giving basic results, the authors generalize the standard concept of descent algebra. One of the valuable results that the authors come up with is constructing subalgebras from the usual group algebra of the Weyl group using a useful device which is a surjective morphim on \(\mathbb{Z}\text{-Irr}(W_n)\). The combinatorial aspect of the construction is demonstrated in a parallel way. Overall, this work is informative and profound.
reviewed by: A. Aljouiee
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 5015304
zbMATH Keywords: descent algebras
zbMATH Keywords: hyperoctahedral groups
zbMATH Keywords: coplactic algebras
zbMATH Keywords: group algebras
zbMATH Keywords: Weyl groups
zbMATH Keywords: Solomon algebras
zbMATH Keywords: irreducible characters of symmetric groups
zbMATH Keywords: Specht modules
describes a project that uses: CHEVIE
MaRDI profile type: Publication
OpenAlex ID: W2949127789
cites work: A symmetry of the descent algebra of a finite Coxeter group.
cites work: Q4652649
cites work: Left cells in type 𝐵_{𝑛} with unequal parameters
cites work: Q3941610
cites work: ON THE INDUCTION OF KAZHDAN–LUSZTIG CELLS
cites work: CHEVIE -- A system for computing and processing generic character tables
cites work: Q4509026
cites work: Q4141936
cites work: Q3998721
cites work: Q4267501
cites work: Q3665331
cites work: Characters of Reductive Groups over a Finite Field. (AM-107)
cites work: Q4399987
cites work: Duality between quasi-symmetric functions and the Solomon descent algebra
cites work: A generalization of solomon’s algebra for hyperoctahedral groups and other wreath products
cites work: Q4844910
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: Q4481862
cites work: Some aspects of groups acting on finite posets
cites work: Q4536185
DOI: 10.5802/AIF.2176
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 5015304