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We study the supersymmetry $U_q(\hat{sl}(M+1|N+1))$ analogue of thesupersymmetric t-J model with a boundary, in the framework of the algebraicanalysis method. We diagonalize the commuting transfer matrix by using thebosonization of the vertex operator associated with the quantum affinesupersymmetry.

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