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 $G\wr\mathfrak{S}_n$

Authors: Pierre Baumann and Christophe Hohlweg
Journal: Trans. Amer. Math. Soc. 360 (2008), 1475-1538
MSC (2000): Primary 16S99; Secondary 05E05, 05E10, 16S34, 16W30, 20B30, 20E22
DOI: https://doi.org/10.1090/S0002-9947-07-04237-7
Published electronically: October 22, 2007
MathSciNet review: 2357703
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Abstract: We propose an analogue of Solomon's descent theory for the case of a wreath product $G\wr\mathfrak{S}_n$ , where 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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