A semigroup approach to wreath-product extensions of Solomon's descent algebras.
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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.
DOI :
10.37236/110
Classification :
20C30, 05E05, 20M25, 20C05, 16S34, 05E10
Mots-clés : wreath products, symmetric groups, invariant algebras, semigroup algebras, group algebras, colored descent algebras
Mots-clés : wreath products, symmetric groups, invariant algebras, semigroup algebras, group algebras, colored descent algebras
@article{10_37236_110,
author = {Samuel K. Hsiao},
title = {A semigroup approach to wreath-product extensions of {Solomon's} descent algebras.},
journal = {The electronic journal of combinatorics},
year = {2009},
volume = {16},
number = {1},
doi = {10.37236/110},
zbl = {1209.20008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/110/}
}
Samuel K. Hsiao. A semigroup approach to wreath-product extensions of Solomon's descent algebras.. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/110
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