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# Generalized Descent Algebras

Published:2007-12-01
Printed: Dec 2007
• Christophe Hohlweg
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## Abstract

If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-$\ZM$-module $\DC_A(W)$ of the group algebra $\ZM W$. 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: Coxeter group, Solomon descent algebra, descent set
 MSC Classifications: 20F55 - Reflection and Coxeter groups [See also 22E40, 51F15] 05E15 - Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]