Bethe vectors of quantum integrable models based on Uq(gl(N))

Abstract

We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by certain morphisms of the positive Borel subalgebra in Uq(gl(N)) into analogous subalgebra in Uq'(gl(N)), with q'=1/q.

Cited by in corpus (13)

• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Asymptotic behaviour of two-point functions in multi-species models
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• Scalar products in models with $GL(3)$ trigonometric $R$-matrix. General case
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• 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
• Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis