  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.
