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

  • Chris Berg (a1), Nantel Bergeron (a2) (a3), Franco Saliola (a1), Luis Serrano (a1) and Mike Zabrocki (a2) (a3)...

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.

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References

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