Highest coefficient of scalar products in SU(3)-invariant integrable models

TL;DR

This paper investigates scalar products in SU(3)-invariant integrable models, providing new sum-over-partitions and integral representations for their highest coefficients, advancing the understanding of their algebraic structure.

Contribution

It introduces novel sum and integral representations for the highest coefficients of scalar products in SU(3) models, enhancing computational and theoretical tools.

Findings

Derived sum-over-partitions representations

Developed multiple integral formulas

Enhanced understanding of algebraic Bethe ansatz

Abstract

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.