A semigroup approach to wreath-product extensions of Solomon's descent algebras

2007/10/10 by Hsiao, Samuel K. · 1 citation
#05E99 #16S34 #20M25 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0710.2081

Abstract

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup Sigma_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 Sigma_n^G into the group algebra of G wr S_n. The generalized descent algebras of Mantaci and Reutenauer are obtained as homomorphic images when G is abelian.

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