| The gl(1|1) supersymmetric vertex model is one of the most important physics models, which is relevant to the strongly correlated electronic systems and high temperature superconductivity. It has been extensively studied in the periodic boundary conditions. For an integrable system, it is more important for physicists to study spectrum of energy and correlation functions. It is well-known that the exact solution and spectrum of energy can be obtained through the algebraic Bethe ansatz, and correlation functions can be also derived with the help of the determinant representation of the scalar product of the Bethe eigenstates in the periodic boundary conditions. The gl(1|1) supersymmetric vertex model is an exactly solvable model not only in the periodic boundary conditions, but also in the domain wall boundary conditions. Its partition function has been represented as determinant of usual functions with the spectral parameters in the domain wall boundary conditions. In this paper, we will consider this model in the domain wall boundary conditions, and calculate its boundary correlation functions by means of the determinant representation of partition function.In this paper, the gl(1|1) supersymmetric vertex model with domain wall boundary conditions (DWBC) on an N×N square lattice is considered. Using the algebraic Bethe ansatz, we derive out the reduction formulae for the one-point boundary correlation functions of the model. At the same time, the recursion relation for the partition function follows from these formulae as a particular case. It is shown that these functions is expressed as the determinants of N×N matrices. Using the similar approach, we also obtain the two-point boundary correlation functions, in terms of the one-point boundary correlation functions of the model. The determinant representation of correlation functions is helpful for us to obtain linear differential equation to be satisfied, and to study its asymptotic behaviors.
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