General scalar products in the arbitrary six-vertex model

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the asymmetric six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. In turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.