Recurrence relations for off-shell Bethe vectors in trigonometric integrable models

TL;DR

This paper develops recurrence relations for off-shell Bethe vectors in quantum integrable models with $U_q( ext{gl}_N)$ symmetry, using the zero modes method to analyze their structure and scalar products.

Contribution

It introduces a novel application of the zero modes method to derive recurrence relations for off-shell Bethe vectors in trigonometric integrable models.

Findings

Derived explicit action formulas for monodromy matrix entries on Bethe vectors.

Established recurrence relations for off-shell Bethe vectors and their scalar product coefficients.

Enhanced understanding of the algebraic structure of Bethe vectors in quantum integrable systems.

Abstract

The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q(\mathfrak{gl}_N)$-invariant $R$-matrices. The action formulas allow to get recurrence relations for off-shell Bethe vectors and for highest coefficients of the Bethe vectors scalar product.