A Solomon descent theory for the wreath products $G\wr \mathfrak S_n$
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- by Pierre Baumann and Christophe Hohlweg PDF
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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.References
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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
- MR Author ID: 685087
- Email: chohlweg@fields.utoronto.ca
- 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: https://doi.org/10.1090/S0002-9947-07-04237-7
- MathSciNet review: 2357703