Dual wavefunction of the Felderhof model

TL;DR

This paper explores the dual wavefunction of the Felderhof six-vertex model, establishing its connection to Schur and factorial Schur polynomials and providing combinatorial formulas and representations.

Contribution

It introduces a dual wavefunction analysis, proving its relation to Schur polynomials and Gelfand-Tsetlin patterns, and generalizes to factorial Schur polynomials.

Findings

Exact correspondence between dual wavefunction and Schur polynomials

Dual wavefunction expressed via strict Gelfand-Tsetlin patterns

Dual version of the Tokuyama combinatorial formula

Abstract

We study the Felderhof free-fermion six-vertex model, whose wavefunction recently turned out to possess rich combinatorial structure of the Schur polynomials. We investigate the dual version of the wavefunction in this paper, which seems to be a harder object to analyze. We evaluate the dual wavefunction in two ways. First, we give the exact correspondence between the dual wavefunction and the Schur polynomials, for which two proofs are given. Next, we make a microscopic analysis and express the dual wavefunction in terms of strict Gelfand-Tsetlin pattern. As a consequence of these two ways of evaluation of the dual wavefunction, we obtain a dual version of the Tokuyama combinatorial formula for the Schur polynomials. We also give a generalization of the correspondence between the dual wavefunction of the Felderhof model and the factorial Schur polynomials.