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

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 $q=0$.