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

  Published:2013-06-21
 Printed: Jun 2014
  • Chris Berg,
    Université du Québec à Montréal, Montréal, QC, Canada
  • Nantel Bergeron,
    York University, Toronto, ON, Canada
  • Franco Saliola,
    Université du Québec à Montréal, Montréal, QC, Canada
  • Luis Serrano,
    Université du Québec à Montréal, Montréal, QC, Canada
  • Mike Zabrocki,
    York University, Toronto, ON, Canada
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Abstract

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 which 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: Hall-Littlewood polynomial, symmetric function, quasisymmetric function, tableau Hall-Littlewood polynomial, symmetric function, quasisymmetric function, tableau
MSC Classifications: 05E05 show english descriptions Symmetric functions and generalizations 05E05 - Symmetric functions and generalizations
 

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