Paper Info
Title
A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras.
Abstract
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 F(n)(G) associated with G(sic)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 F(n)(G) into the group algebra of G(sic)S(n). The colored descent algebras of Mantaci and Reutenauer are obtained as homomorphic images when G is abelian.
Year
Venue
Keywords
2009
ELECTRONIC JOURNAL OF COMBINATORICS
group algebra,wreath product,symmetric group
Field
DocType
Volume
Subalgebra,Discrete mathematics,Abelian group,Combinatorics,Braid,Symmetric group,Group algebra,Wreath product,Semigroup,Combinatorial model,Mathematics
Journal
16.0
Issue
ISSN
Citations 
1.0
1077-8926
0
PageRank 
References 
Authors
0.34
3
1
Name
Order
Citations
PageRank
Samuel K. Hsiao172.34