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A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions

Published online by Cambridge University Press:  20 November 2018

Chris Berg ,
Nantel Bergeron ,
Franco Saliola ,
Luis Serrano  and
Mike Zabrocki
Chris Berg
Affiliation:
Université du Québec à Montréal, Montréal, QC. e-mail: cberg@lacim.ca, saliola.franco@uqam.ca, serrano@lacim.ca
Nantel Bergeron
Affiliation:
Fields Institute, TorontoON York University, TorontoON. e-mail: bergeron@mathstat.yorku.ca, zabrocki@mathstat.yorku.ca
Franco Saliola
Affiliation:
Université du Québec à Montréal, Montréal, QC. e-mail: cberg@lacim.ca, saliola.franco@uqam.ca, serrano@lacim.ca
Luis Serrano
Affiliation:
Université du Québec à Montréal, Montréal, QC. e-mail: cberg@lacim.ca, saliola.franco@uqam.ca, serrano@lacim.ca
Mike Zabrocki
Affiliation:
Fields Institute, TorontoON York University, TorontoON. e-mail: bergeron@mathstat.yorku.ca, zabrocki@mathstat.yorku.ca
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Abstract

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We introduce a new basis of the algebra of non-commutative symmetric functions whose images under the forgetful map are Schur functions when indexed by a partition. Dually, we build a basis of the quasi-symmetric functions that expand positively in the fundamental quasi-symmetric functions. We then use the basis to construct a non-commutative lift of the Hall–Littlewood symmetric functions with similar properties to their commutative counterparts.

Keywords

05E05Hall-Littlewood polynomialsymmetric functionquasisymmetric functiontableau
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 3 , 01 June 2014 , pp. 525 - 565
Copyright
Copyright © Canadian Mathematical Society 2014

References

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