Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models

Understand

We study the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots.

• We construct recursion relations relating S_{l,m} to scalar products of smaller dimension, namely S_{l-1,m} and S_{l,m-1}.
• Solving these recursion relations we obtain new multiple integral expressions for S_{l,m}, whose integrands are (l+m) \times (l+m) determinants, and closely related to the Slavnov determinant expression for the SU(2) scalar product.