The factorized F-matrices for arbitrary U(1)(N−1) integrable vertex models

We discuss the F-matrices associated to the R-matrix of a general N-state vertex model whose statistical configurations encode N−1U(1) symmetries. The factorization condition is shown for arbitrary weights being based only on the unitarity property and the Yang-Baxter relation satisfied by the R-matrix. Focusing on the N=3 case we are able to conjecture the structure of some relevant twisted monodromy matrix elements for general weights. We apply this result providing the algebraic expressions of the domain wall partition functions built up in terms of the creation and annihilation monodromy fields. For N=3 we also exhibit a R-matrix whose weights lie on a del Pezzo surface and have a rather general structure.