Published in
Cambridge University Press, Canadian Journal of Mathematics, 3(66), p. 525-565, 2014
Links
Tools
A Lift of the Schur and Hall-Littlewood Bases to Non-commutative Symmetric Functions
,
Franco Saliola,
Luis Serrano,
Mike Zabrocki
Full text: Download
Abstract
AbstractWe 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.