# Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A^{(1)}_{n-1}$

## TL;DR

This paper introduces a systematic method for solving the set-theoretical reflection equation using known solutions to the Yang-Baxter equation, with applications to crystals related to quantum affine algebras.

## Contribution

It presents a novel approach to derive solutions for the reflection equation from existing Yang-Baxter solutions, specifically for type $A^{(1)}_{n-1}$ quantum affine algebras.

## Key findings

- Examples from crystals and geometric crystals are provided.
- The method successfully produces solutions for the reflection equation.
- Applications to quantum affine algebra structures are demonstrated.

## Abstract

A trick to obtain a systematic solution to the set-theoretical reflection equation is presented from a known one to the Yang-Baxter equation. Examples are given from crystals and geometric crystals associated to the quantum affine algebra of type $A^{(1)}_{n-1}$.