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Generalized Descent Algebras

Published online by Cambridge University Press:  20 November 2018

Christophe Hohlweg
Christophe Hohlweg*
Affiliation:
The Fields Institute, 222 College Street, Toronto, ON, M5T 3J1 e-mail: chohlweg@fields.utoronto.ca
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Abstract

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If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-$\mathbb{Z}$-module ${{\mathcal{D}}_{A}}\left( W \right)$ of the group algebra $\mathbb{Z}W$. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type $B$, the Mantaci–Reutenauer algebra.

Keywords

20F5505E15Coxeter groupSolomon descent algebradescent set
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 4 , 01 December 2007 , pp. 535 - 546
Copyright
Copyright © Canadian Mathematical Society 2007

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