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Around Solomon’s descent algebras. (English) Zbl 1193.20046
Summary: We study different problems related to Solomon’s descent algebra $$\Sigma(W)$$ of a finite Coxeter group $$(W,S)$$: positive elements, morphisms between descent algebras, Loewy length…. One of the main result is that, if $$W$$ is irreducible and if the longest element is central, then the Loewy length of $$\Sigma(W)$$ is equal to $$\Bigl\lceil\tfrac{|S|}{2}\Bigr\rceil$$.

##### MSC:
 20F55 Reflection and Coxeter groups (group-theoretic aspects) 05E10 Combinatorial aspects of representation theory 05E15 Combinatorial aspects of groups and algebras (MSC2010) 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 20C30 Representations of finite symmetric groups
CHEVIE
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