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We present the expressions for the monodromy matrix elements of thesix-vertex model in the F-basis for arbitrary Boltzmann weights. The resultsrely solely on the property of unitarity and Yang-Baxter relations, avoidingany specific parameterization of the weights. This allows us to write completealgebraic expressions for the inner products and the underlying domain wallpartition functions in the case of arbitrary rapidities. We then apply ourresults for the trigonometric six-vertex model in the presence of inhomogeneouselectric fields and obtain a determinant formula for the respective on-shellscalar products.

The monodromy matrix in the F-basis for arbitrary six-vertex models