A combinatorial proof of the Giambelli identity for Schur functions

AbstractThe Giambelli identity provides a formula for expressing an arbitrary Schur function of shape λ as a determinant of Schur functions of hook shapes (l, 1k). We give the first complete combinatorial proof of the Giambelli identity. We show how to derive various hook formulas from the Giambelli identity and show how to extend our methods to derive extensions of the Giambelli identity and the hook formula for the number of standard tableaux to certain skew shapes