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

By Ronald C. King, Trevor A. Welsh and Stephanie J. van Willigenberg

Abstract

Some new relations on skew Schur function differences are established both combinatorially using Sch\"utzenberger'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

Topics: QA
Year: 2008
OAI identifier: oai:eprints.soton.ac.uk:66210
Provided by: e-Prints Soton
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