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

By Chris Berg, Nantel Bergeron, Franco V. Saliola, Luis G. Serrano, Mike Zabrocki. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2012

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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 that 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

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