Stembridge's Schur-positivity conjecture for monomial immanants

Let a Jacobi–Trudi matrix be the matrix whose determinant is the skew-Schur function of a skew shape, and let a monomial immanant be the immanant obtained by using the virtual character corresponding to a monomial symmetric function under the Frobenius characteristic map. A symmetric function is Schur-positive if its expansion in the Schur-function basis has non-negative integer coefficients.

Stembridge's conjecture. Monomial immanants of Jacobi–Trudi matrices are Schur-positive.

Ordinary immanants are known to be Schur-positive by Haiman's theorem, while this related assertion for monomial immanants is the conjecture considered in the paper. It concerns positivity in the Schur basis for a broad class of immanants associated with Jacobi–Trudi matrices.