A Solomon descent theory for the wreath products G ~ S_n
Combinatorics
2011-12-20 v1 Rings and Algebras
Abstract
We propose an analogue of Solomon's descent theory for the case of a wreath product G ~ S_n, where G is a finite abelian group. Our construction mixes a number of ingredients: Mantaci-Reutenauer algebras, Specht's theory for the representations of wreath products, Okada's extension to wreath products of the Robinson-Schensted correspondence, Poirier's quasisymmetric functions. We insist on the functorial aspect of our definitions and explain the relation of our results with previous work concerning the hyperoctaedral group.
Keywords
Cite
@article{arxiv.math/0503011,
title = {A Solomon descent theory for the wreath products G ~ S_n},
author = {Pierre Baumann and Christophe Hohlweg},
journal= {arXiv preprint arXiv:math/0503011},
year = {2011}
}