The Smith Normal Form of a Specialized Jacobi-Trudi Matrix

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Let JTλ be the Jacobi-Trudi matrix corresponding to the partition λ, so λ is the Schur function sλ in the variables x₁,x₂,. Set x₁==xₙ=1 and all other xᵢ=0. Then the entries of JTλ become polynomials in n of the form n+j-1 j. We determine the Smith normal form over the ring Q[n] of this specialization of JTλ. The proof carries over to the specialization xᵢ=qⁱ⁻¹ for 1≤ i≤ n and xᵢ=0 for i>n, where we set qⁿ=y and work over the ring Q(q)[y].