Unimodality of Differences of Specialized Schur Functions

Authors:
V. Reiner;D. Stanton
Affiliations:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455;School of Mathematics, University of Minnesota, Minneapolis, MN 55455
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1998

Citing 3
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Abstract

The centered difference of principally specialized Schur functionss_˜λ(1,q,....,q^n) -q^ns_λ(1,q,....,q^n) is shownto be a symmetric, unimodal polynomial in q with non-negative coefficientsfor certain choices of ˜λ, λ, and n, in which˜λ is always obtained from λ by adding two cells, and nis chosen to be odd or even depending on ˜λ, λ. Thebasic technique is to find an injection of representations for thesymplectic or orthogonal Lie algebras, and interpret the above difference asthe principal specialization of the formal character of the quotient. As aspecial case, a difference of q-binomial coefficients is shown to beunimodal.