A compound determinant identity for rectangular matrices and determinants of Schur functions

A compound determinant identity for minors of rectangular matrices is established. Given an (s+n−1)×sn(s+n−1)×sn matrix A with s blocks of n columns, we consider minors of A by picking up in each block the first consecutive columns specified by weak compositions at most s   parts, and prove that the compound determinant of such n×nn×n minors of A is equal to the product of maximal minors of A   corresponding to compositions of s+n−1s+n−1 with s parts. As an application, we obtain Vandermonde type product evaluations of determinants of classical group characters, including Schur functions.