Universal Bethe Ansatz and Scalar Products of Bethe Vectors

An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_3)$ is given. This result is obtained in the framework of the universal Bethe ansatz, using presentation of the universal Bethe vectors in terms of the total currents of a “new” realization of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_3)$.