# Dual wavefunction of the symplectic ice

## TL;DR

This paper extends the integrable six-vertex model to reflecting boundaries, establishing a precise link between dual wavefunctions and symplectic Schur functions, and generalizes to factorial symplectic Schur functions via inhomogeneous models.

## Contribution

It introduces a dual wavefunction framework for the symplectic ice model with reflecting boundaries, connecting it to symplectic Schur functions and their factorial generalizations.

## Key findings

- Exact correspondence between dual wavefunction and symplectic Schur functions.
- Extension of the model to reflecting boundary conditions.
- Generalization to factorial symplectic Schur functions with inhomogeneity.

## Abstract

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.