# Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis

## TL;DR

This paper extends the Izergin-Korepin analysis to analyze wavefunctions of the six-vertex model with triangular boundary conditions, providing explicit symmetric function representations and characterizations.

## Contribution

It introduces an analogue of wavefunctions for the six-vertex model with triangular boundary and determines their explicit symmetric function form using extended Izergin-Korepin analysis.

## Key findings

- Explicit symmetric functions for wavefunctions derived
- Characterization of wavefunctions with triangular boundary established
- Analysis extended to ordinary wavefunctions as a basic case

## Abstract

We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and a special class of the triangular $K$-matrix, we first introduce an analogue of the wavefunctions of the integrable six-vertex model with triangular boundary. We first give a characterization of the wavefunctions by extending our recent work of the Izergin-Korepin analysis of the domain wall boundary partition function with triangular boundary, and then determine the explicit form of the symmetric functions representing the wavefunctions by showing that it satisfies all the required properties. We also illustrate the Izergin-Korepin analysis for the case of ordinary wavefunctions as it is the basic case.