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

Berg, Chris ; Bergeron, Nantel ; Saliola, Franco ; Serrano, Luis ; Zabrocki, Mike

Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 525-565

Résumé

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.

Détail

DOI : 10.4153/CJM-2013-013-0

Mots-clés : 05E05, Hall-Littlewood polynomial, symmetric function, quasisymmetric function, tableau

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