A Solomon descent theory for the wreath products 𝐺≀𝔖_{𝔫}

Baumann, Pierre; Hohlweg, Christophe

doi:10.1090/S0002-9947-07-04237-7

A Solomon descent theory for the wreath products $G\wr \mathfrak S_n$
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by Pierre Baumann and Christophe Hohlweg PDF

Trans. Amer. Math. Soc. 360 (2008), 1475-1538 Request permission

Abstract:

We propose an analogue of Solomon’s descent theory for the case of a wreath product $G\wr \mathfrak S_n$, 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, and 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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