Refection Matrices for the (n+1)(2n+1)- Vertex Models: Diagonal Solutions

TL;DR

This paper derives diagonal solutions for reflection equations in a class of vertex models with complex vertex counts, expanding understanding of integrable systems with boundary conditions.

Contribution

It introduces a method to find diagonal K matrix solutions for vertex models with (n+1)(2n+1) vertices, based on two sets of R matrices solving Yang-Baxter equations.

Findings

Derived n!-rac{1}{2}(n-2)(n-1) diagonal K matrices for each n

Extended the class of solvable models with boundary conditions

Provided explicit solutions for complex vertex models

Abstract

We have find the diagonal K matrix solutions of the reflection equations for a class of vertex models. These models have (n+1)(2n+1) vertices and are defined as two set of (n + 1) R matrices, solutions of the equations of Yang-Baxter equations. For a given value of \text{n} we find n!-\frac{1}{2}(n-2)(n-1) K diagonal matrices.