  Factorial Schur functions are generalizations of Schur functions that have,
in addition to the usual variables, a second family of "shift" parameters. We
show that a factorial Schur function times a deformation of the Weyl
denominator may be expressed as the partition function of a particular
statistical-mechanical system (six vertex model). The proof is based on the
Yang-Baxter equation. There is a deformation parameter $t$ which may be
specialized in different ways. If $t=-1$, then we recover the expression of the
factorial Schur function as a ratio of alternating polynomials. If $t=0$, we
recover the description as a sum over tableaux. If $t=\infty$ we recover a
description of Lascoux that was previously considered by McNamara. We also are
able to prove using the Yang-Baxter equation the asymptotic symmetry of the
factorial Schur functions in the shift parameters. Finally, we give a proof
using our methods of the dual Cauchy identity for factorial Schur functions.
Thus using our methods we are able to give thematic proofs of many of the
properties of factorial Schur functions.
