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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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:
  • 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
  • MR Author ID: 685087
  • Email:
  • 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
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1475-1538
  • MSC (2000): Primary 16S99; Secondary 05E05, 05E10, 16S34, 16W30, 20B30, 20E22
  • DOI:
  • MathSciNet review: 2357703