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Abstract:
We define a symmetric function to be be Schur nonnegative (SNN)
if it is equal to a nonnegative linear combination of Schur functions.
We define a polynomial p(x_11, ..., x_nn) in n^2 variables to be Schur
nonnegative if for every Jacobi-Trudi matrix A = (a_ij), the symmetric
function p(a_11, ..., a_nn) is SNN. Using the Kazhdan-Lusztig basis for
C[S_n], we will show that certain differences of products of matrix minors
are SNN. From this fact we will deduce new inequalities similar to those
recently conjectured by Fomin-Fulton-Li-Poon and will interpret these
inequalities in terms of the Grassmannian variety.
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