Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors

Abstract

Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the $\mathfrak{gl}(m|n)$-invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the sum formula for the scalar product. For simplicity, detailed proofs are given for the $\mathfrak{gl}(m)$ case. The results for the supersymmetric case can be obtained similarly and are formulated without proofs.

arXiv comment28 pages

References in corpus (8)

• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• Bethe vectors for orthogonal integrable models
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors

Cited by in corpus (5)

• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Gauss Coordinates vs Currents for the Yangian Doubles of the Classical Types
• On the R-matrix realization of quantum loop algebras
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models