noindent “Integrability meeting ENS/IPhT'' We consider a problem of Bethe vectors scalar products of the models solvable by the (nested) algebraic Bethe ansatz. For the models with gl(2) symmetry or its q-deformation, the scalar products can be calculated straightforwardly via the standard arguments of the algebraic Bethe ansatz. However, for the models with higher rank symmetry, the technical complexity of such a calculation increases immensely. We suggest a new method based on the coproduct properties of the Bethe vectors. We illustrate this method by the example of the scalar products in the gl(2) based models. (IPhT organizer: Ivan Kostov)

Steklov Mathematical Inst. of Russian Academy of Sciences, Moscow