Abstract We show that the scalar products of on-shell and off-shell Bethe vectors in the algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also apply our method to the XXX spin chain with broken U(l) symmetry.
Abstract We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing gl ( 2 ∣ 1 ) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with gl ( 1 ∣ 1 ) symmetry.