# Solutions of the $U_q(\widehat{\mathfrak{sl}}_N)$ reflection equations

## TL;DR

This paper classifies all invertible solutions to the reflection equations associated with the Bazhanov-Jimbo R-matrix for type A^{(1)}_{N-1}, demonstrating they can be derived from constant solutions via affinization.

## Contribution

It provides a complete classification of invertible solutions to both untwisted and twisted reflection equations for a specific quantum affine algebra.

## Key findings

- All invertible solutions are obtained through affinization of constant solutions.
- The solutions cover both untwisted and twisted reflection equations.
- The classification applies to the Bazhanov-Jimbo R-matrix of type A^{(1)}_{N-1}.

## Abstract

We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an appropriate affinization procedure from solutions of the constant untwisted and twisted reflection equations.

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Source: https://tomesphere.com/paper/1803.06491