Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes

Authors:
Ronald C. King;Trevor A. Welsh;Stephanie J. Willigenburg
Affiliations:
School of Mathematics, University of Southampton, Hampshire, UK SO17 1BJ;Department of Physics, University of Toronto, Toronto, Canada M5S 1A7;Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2008

Citing 4
Cited 2

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Abstract

Some new relations on skew Schur function differences are established both combinatorially using Schützenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive.