# Izergin-Korepin analysis on the projected wavefunctions of the generalized free-fermion model

## TL;DR

This paper extends the Izergin-Korepin analysis to the projected wavefunctions of a generalized free-fermion model, revealing they can be expressed via symmetric functions generalizing factorial Schur functions, thus broadening the understanding of integrable models.

## Contribution

It introduces a generalized L-operator for the six-vertex model and characterizes the projected wavefunctions as products and symmetric functions, generalizing the Tokuyama formula.

## Key findings

- Projected wavefunctions expressed as products and symmetric functions
- Generalization of the factorial Schur functions
- Extension of the Tokuyama formula

## Abstract

We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the $L$-operator of the six-vertex model by Bump-Brubaker-Friedberg and Bump-McNamara-Nakasuji. We make the Izergin-Korepin analysis to characterize the projected wavefunctions and show that they can be expressed as a product of factors and certain symmetric functions which generalizes the factorial Schur functions. This result can be seen as a generalization of the Tokuyama formula for the factorial Schur functions.