Bethe vectors of quantum $U_q(gl_N)$-invariant integrable models

S. Pakuliak, E. Ragoucy, N. A. Slavnov

Published Jan 1, 2014• 1 citation

Abstract

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

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Bethe vectors of quantum $U_q(gl_N)$ -invariant integrable modelsBethe vectors of quantum $U_q(gl_N)$-invariant integrable models

S. Pakuliak, E. Ragoucy, N. A. Slavnov

Published Jan 1, 2014• 1 citation

OpenAlex

Abstract

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Bethe vectors of quantum

U_q(gl_N)

-invariant integrable models

Bethe vectors of quantum integrable models based on

U_q(\widehat{\mathfrak {gl}}_{N})

On Bethe vectors in

\mathfrak{g}{\mathfrak{l}}_3

-invariant integrable models

Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing

\mathfrak{g}{\mathfrak{l}}_3

g l 3 -invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters. They thus do become on-shell vectors provided the system of Bethe equations is fulfilled.