Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A^{(1)}_{n-1})$

Abstract: We present a new solution to the reflection equation associated with a coideal subalgebra of $U_q(A^{(1)}_{n-1})$ in the symmetric tensor representations and their dual. Elements of the $K$ matrix are expressed by a matrix product formula involving terminating $q$-hypergeometric series in $q$-boson generators. At $q=0$, our result reproduces a known set-theoretical solution to the reflection equation connected to the crystal base theory.