Reflection algebra and functional equations

TL;DR

This paper explores the use of reflection algebra to derive functional equations for the six-vertex model's partition function, providing integral representations and differential equations that facilitate analysis.

Contribution

It introduces a novel approach using reflection algebra to obtain functional relations and integral formulas for the six-vertex model with boundary conditions.

Findings

Derived functional relations for the partition function

Expressed the partition function as a multiple-contour integral

Established partial differential equations from the functional relations

Abstract

In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall boundary conditions and one reflecting end. The model's partition function is expressed as a multiple-contour integral that allows the homogeneous limit to be obtained straightforwardly. Our functional equations are also shown to give rise to a consistent set of partial differential equations for the partition function.