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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
Published electronically: October 22, 2007
MathSciNet review: 2357703
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Pierre Baumann
Affiliation: Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France

Christophe Hohlweg
Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Address at time of publication: Université du Québec à Montréal, Case postale 8888, succursale Centre-ville, Montréal, Québec, Canada H3C 3P8

Keywords: Wreath products, Solomon descent algebra, quasisymmetric functions.
Received by editor(s): April 1, 2005
Received by editor(s) in revised form: December 2, 2005
Published electronically: October 22, 2007
Additional Notes: This work was partially supported by Canada Research Chairs
Article copyright: © Copyright 2007 American Mathematical Society

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