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

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

2007-10-10

arxiv.org/abs/0710.2081v2

Mathematics

Rings and Algebras

6 pages, added a reference and updated the Introduction

Scientific paper

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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