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