Diagonalization of transfer matrix of supersymmetry $u_q(\widehat{sl}(m+1\mathrm{\mid }n+1))$ chain with a boundary

We study the supersymmetry $U_q(\widehat{sl}(M+1\mathrm{\mid }N+1))$ analogue of the supersymmetric t-J model with a boundary, in the framework of the algebraic analysis method. We diagonalize the commuting transfer matrix by using the bosonization of the vertex operator associated with the quantum affine supersymmetry.