Diagonalization of boundary transfer matrix for the $U_{q,p}(\widehat{sl}(3,\mathbf{C}))$ ABF model

We construct a free field realization of the ground state of the boundary transfer matrix for the $U_{q,p}({\widehat{sl}}_3)$ ABF model. Using this ground state and type-II vertex operator, we have a diagonalization of the boundary transfer matrix.