  The six-vertex model on an $N\times N$ square lattice with domain wall
boundary conditions is considered. A Fredholm determinant representation for
the partition function of the model is given. The kernel of the corresponding
integral operator is of the so-called integrable type, and involves classical
orthogonal polynomials. From this representation, a ``reconstruction'' formula
is proposed, which expresses the partition function as the trace of a suitably
chosen quantum operator, in the spirit of corner transfer matrix and vertex
operator approaches to integrable spin models.
