A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions
Authors:
- Chris BergCBChris Berg
- Nantel BergeronNBNantel Bergeron
- Franco SaliolaFSFranco Saliola
- Luis SerranoLSLuis Serrano
- Mike ZabrockiMZMike Zabrocki
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- 1 June 2014
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 66 (3) , 525-565
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 theHall–Littlewood symmetric functions with similar properties to their commutative counterparts.Keywords
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This publication has 23 references indexed in Scilit:
- Skew quasisymmetric Schur functions and noncommutative Schur functionsAdvances in Mathematics, 2011
- From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrixEuropean Journal of Combinatorics, 2010
- Combinatorial Hopf algebras, noncommutative Hall–Littlewood functions, and permutation tableauxAdvances in Mathematics, 2010
- Hall–Littlewood Vertex Operators and Generalized Kostka PolynomialsAdvances in Mathematics, 2001
- Rodrigues Formulas for the Macdonald PolynomialsAdvances in Mathematics, 1997
- Duality between Quasi-Symmetrical Functions and the Solomon Descent AlgebraJournal of Algebra, 1995
- Noncommutative Symmetrical FunctionsAdvances in Mathematics, 1995
- Vertex operators and Hall-Littlewood symmetric functionsAdvances in Mathematics, 1991
- Vertex operators, symmetric functions, and the spin group ΓnJournal of Algebra, 1991
- On the Number of Reduced Decompositions of Elements of Coxeter GroupsEuropean Journal of Combinatorics, 1984