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{\bf Samuel K. Hsiao}
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{\bf A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras}
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There is a well-known combinatorial model, based on ordered set
partitions, of the semigroup of faces of the braid arrangement. We
generalize this model to obtain a semigroup ${\cal F}_n^G$ associated
with $G\wr S_n$, the wreath product of the symmetric group $S_n$ with
an arbitrary group $G$. Techniques of Bidigare and Brown are adapted
to construct an anti-homomorphism from the $S_n$-invariant subalgebra
of the semigroup algebra of ${\cal F}_n^G$ into the group algebra of
$G\wr S_n$. The colored descent algebras of Mantaci and Reutenauer are
obtained as homomorphic images when $G$ is abelian.



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