Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes
Ronald C. King1
, Trevor A. Welsh2
and Stephanie J. Van Willigenburg3
1University of Southampton School of Mathematics University Road, Southampton Hampshire SO17 1BJ UK
2University of Toronto Department of Physics 60 St. George Street Toronto ON M5S 1A7 Canada
3University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada
2University of Toronto Department of Physics 60 St. George Street Toronto ON M5S 1A7 Canada
3University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada
DOI: 10.1007/s10801-007-0113-0
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.
Pages: 139–167
Keywords: keywords Jacobi-trudi determinant; jeu de taquin; ribbon; Schubert calculus; Schur positive; skew Schur function; symmetric function
Full Text: PDF
References
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34. Am. Math. Soc., Providence (1984)
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