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A Solomon descent theory for the wreath products G ~ S_n

Pierre Baumann·Christophe Hohlweg
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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.

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Pierre Baumann, Christophe Hohlweg. 2005-03-01. A Solomon descent theory for the wreath products G ~ S_n. https://arxiv.org/abs/math/0503011

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