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

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

2007-06-22

arxiv.org/abs/0706.3253v2

Mathematics

Combinatorics

30 pages; final version to appear in Journal of Algebraic Combinatorics, Manfred Schocker Memorial Volume

Scientific paper

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.

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