  The wavefunction of the free-fermion six-vertex model was found to give a
natural realization of the Tokuyama combinatorial formula for the Schur
polynomials by Bump-Brubaker-Friedberg. Recently, we studied the correspondence
between the dual version of the wavefunction and the Schur polynomials, which
gave rise to another combinatorial formula. In this paper, we extend the
analysis to the reflecting boundary condition, and show the exact
correspondence between the dual wavefunction and the symplectic Schur
functions. This gives a dual version of the integrable model realization of the
symplectic Schur functions by Ivanov. We also generalize to the correspondence
between the wavefunction, the dual wavefunction of the six-vertex model and the
factorial symplectic Schur functions by the inhomogeneous generalization of the
model.
