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1. CJM 2013 (vol 66 pp. 525)

Berg, Chris; Bergeron, Nantel; Saliola, Franco; Serrano, Luis; Zabrocki, Mike
A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions
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

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