Non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model

TL;DR

This paper derives a class of non-diagonal solutions to the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model, involving intertwining matrices and multiple boundary parameters.

Contribution

It introduces a new class of solutions expressed via intertwining matrices, expanding understanding of boundary conditions in integrable models.

Findings

Solutions expressed in terms of intertwining matrices and their inverses.

Inclusion of discrete and continuous boundary parameters.

Provides explicit non-diagonal solutions for the reflection equation.

Abstract

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a {\it discrete} (positive integer) parameter $l$, $1\leq l\leq n$, the solution contains $n+2$ {\it continuous} boundary parameters.