Domain wall boundary partition function of the six-vertex model with triangular boundary

TL;DR

This paper introduces a new boundary condition for the six-vertex model, deriving an explicit symmetric function for its partition function using algebraic and graphical methods.

Contribution

It formulates and characterizes the domain wall boundary partition function with triangular boundary using $U_q(sl_2)$ R-matrix and reflection equations, providing an explicit symmetric function.

Findings

Explicit form of the partition function as a symmetric function

Verification of properties via Yang-Baxter and reflection equations

Extension of boundary conditions in integrable models

Abstract

We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$ $R$-matrix and a special class of the triangular $K$-matrix. By using its graphical representation, we make the Izergin-Korepin analysis with the help of the Yang-Baxter relation and the reflection equation to give a characterization of the partition function. The explict form of the symmetric function representing the partition function is presented by showing that it satisfies all the required properties.