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Generalized Descent Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2007
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