Generalized descent algebras
Cedric Bonnafe, Christophe Hohlweg
Abstract
If A is a subset of the set of reflections of a finite Coxeter group W, we define a sub-Z-module DA(W) of the group algebra Z W. We provide examples where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra and, if W if of type B, the Mantaci-Reutenauer algebra.
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