Rational solutions of the Garnier system in terms of Schur polynomials

We present a family of rational solutions of the Garnier system HN and show that the corresponding τ-functions form special polynomials Rm,n(m,n ∈ ℤ≥0) under a certain normalization. We give an explicit formula for the special polynomials Rm,n in terms of the Schur polynomial attached to a rectangular Young diagram.