# Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry

## TL;DR

This paper derives a sum formula and recursion relations for scalar products of Bethe vectors in models with $rak{gl}(m|n)$ symmetry, advancing the algebraic Bethe ansatz framework for superalgebra-based integrable models.

## Contribution

It introduces a new sum formula and recursion relations for scalar products of Bethe vectors in $rak{gl}(m|n)$ models, expanding the algebraic Bethe ansatz methodology.

## Key findings

- Derived a sum formula for scalar products in $rak{gl}(m|n)$ models.
- Established recursion relations for Bethe vectors and their scalar products.
- Provided a framework for calculating scalar products using partitions of Bethe parameters.

## Abstract

We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$ superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of Bethe parameters. We also obtain recursions for the Bethe vectors. This allows us to find recursions for the highest coefficient of the scalar product.