Lagrange Inversion and Schur Functions

Authors:
Cristian Lenart
Affiliations:
Department of Mathematics and Statistics, SUNY at Albany, Albany NY 12222. lenart@csc.albany.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2000

Citing 5
Cited 1

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Abstract

Macdonald defined an involution on symmetric functions byconsidering the Lagrange inverse of the generating function of thecomplete homogeneous symmetric functions. The main result we prove inthis note is that the images of skew Schur functions under thisinvolution are either Schur positive or Schur negative symmetricfunctions. The proof relies on the combinatorics of Lagrangeinversion. We also present a q-analogue of this result, which isrelated to the q-Lagrange inversion formula of Andrews, Garsia, andGessel, as well as the operator ∇ of Bergeron and Garsia.