Scalar products of Bethe vectors in models with symmetry 1. Super-analog of Reshetikhin formula**Dedicated to the memory of Petr Petrovich Kulish.

Abstract

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing 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 symmetry.