A Solomon descent theory for the wreath products
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We propose an analogue of Solomon's descent theory for the case of a wreath product , 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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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:
https://doi.org/10.1090/S0002-9947-07-04237-7
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