Integral formulas and antisymmetrization relations for the six-vertex model

We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation probability can be derived from that for the so-called row configuration probability. A crucial ingredient in the proof is a relation expressing the result of antisymmetrization of some given function with respect to permutations in two sets of its variables in terms of the Izergin-Korepin partition function. This relation generalizes another one obtained by Tracy and Widom in the context of the asymmetric simple exclusion process.