Advances in Mathematics, 70 (1988), pp. 59-86.
Ömer Egecioglu and Jeffrey B. Remmel
A Combinatorial Proof of the Giambelli Identity for Schur Functions
Abstract.
The Giambelli identity provides a formula for expressing an
arbitrary Schur function of shape $\lambda$ as a determinant
of Schur functions of hook shapes $(l,1^k)$. 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.
omer@cs.ucsb.edu