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

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