Bethe Ansatz for the Universal Weight Function

Abstract

We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q({\widehat{gl}}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the product of the transfer matrix and these vectors. We derive that these vectors are eigenvectors of the transfer matrix if their Bethe parameters satisfy the universal Bethe equations [arXiv:math-ph/0512037].

31 pages, 1 figure, misprints corrected and reference added

References in corpus (7)

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Cited by in corpus (19)

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• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
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• Combinatorial Formulae for Nested Bethe Vectors
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Bethe vectors of quantum integrable models based on Uq(gl(N))
• Bethe Ansatz and Bethe Vectors Scalar Products
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• Multiple commutation relations in the models with gl(2|1) symmetry
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Generating Series for Nested Bethe Vectors
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis