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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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: 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
Email: baumann@math.u-strasbg.fr

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
Email: chohlweg@fields.utoronto.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04237-7
PII: S 0002-9947(07)04237-7
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