A lift of the Schur and Hall-Littlewood bases to non-commutative   symmetric functions
  We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur 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. 
Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano, Mike   Zabrocki
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