Toeplitz minors and specializations of skew Schur polynomials

We express minors of Toeplitz matrices of finite and large dimension, including the case of symbols with Fisher-Hartwig singularities, in terms of specializations of symmetric functions. By comparing the resulting expressions with the inverses of some Toeplitz matrices, we obtain explicit formulasfor a Selberg-Morris integral and for specializations of certain skew Schur polynomials.