Solution to the reflection equation related to the $\iota$quantum group of type AII

TL;DR

This paper presents a solution to the reflection equation linked to a specific quantum group coideal subalgebra, revealing a parameter choice where the solution simplifies and aligns with a known classical case.

Contribution

It provides an explicit $K$ matrix solution for the reflection equation associated with a coideal subalgebra of $U_q(A_{2n-1}^{(1)})$ of type AII, including a special parameter setting.

Findings

The $K$ matrix solution is explicitly constructed.

Under certain parameters, the solution becomes independent of $q$.

The solution coincides with a known classical solution at $q=0$.

Abstract

A solution to the reflection equation associated to a coideal subalgebra of $U_q(A_{2n-1}^{(1)})$ of type AII in the symmetric tensor representations is presented. If parameters of the coideal subalgebra are suitably chosen, the $K$ matrix does not depend on the quantum parameter $q$ and still agrees with a solution in arXiv:nlin/0411044 at $q=0$.