Around Solomon's descent algebras.

DOI10.1007/s10468-008-9090-9zbMath1193.20046arXivmath/0601317OpenAlexW1971356396MaRDI QIDQ1029580

J. Blot

Publication date: 13 July 2009

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601317

zbMATH Keywords

parabolic subgroupsLoewy lengthscoset representativesSolomon descent algebrasirreducible finite Coxeter groups

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items

On the left connected subalgebra of the descent algebra of a Coxeter group of classical type ⋮ The Steinberg torus of a Weyl group as a module over the Coxeter complex ⋮ On the quiver presentation of the descent algebra of the symmetric group. ⋮ Representation theory of Mantaci-Reutenauer algebras. ⋮ Semidirect Product Decomposition of Coxeter Groups ⋮ The Loewy length of the descent algebra of type \(D\). ⋮ A quiver presentation for Solomon's descent algebra. ⋮ Unnamed Item

Uses Software

• CHEVIE

Cites Work

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• A symmetry of the descent algebra of a finite Coxeter group.
• A decomposition of the descent algebra of a finite Coxeter group
• Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups. With an appendix by Pierre Baumann and Christophe Hohlweg.
• Representation theory of Mantaci-Reutenauer algebras.
• Homomorphisms between Solomon's descent algebras
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Coxeter orbits and eigenspaces of Frobenius
• CHEVIE -- A system for computing and processing generic character tables
• A generalization of solomon’s algebra for hyperoctahedral groups and other wreath products