arXiv:1310.3253 · Journal of Physics A Mathematical and Theoretical

Bethe vectors of quantum integrable models based on $U_q(\widehat{\mathfrak {gl}}_{N})$

S Pakuliak, E. Ragoucy, N A Slavnov

Published Feb 21, 2014• 27 citations

Abstract

We study quantum 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 into analogous subalgebra in .

DOI: 10.1088/1751-8113/47/10/105202

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arXiv:1310.3253 · Journal of Physics A Mathematical and Theoretical

Bethe vectors of quantum integrable models based on $U_q(\widehat{\mathfrak {gl}}_{N})$ Bethe vectors of quantum integrable models based on $U_q(\widehat{\mathfrak {gl}}_{N})$

S Pakuliak, E. Ragoucy, N A Slavnov

Published Feb 21, 2014• 27 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8113/47/10/105202

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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

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Bethe vectors of quantum integrable models based on

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

Bethe vectors of quantum

U_q(gl_N)

-invariant integrable models

Scalar products and norm of Bethe vectors for 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.

Scalar products of Bethe vectors in models with

\mathfrak{gl}(2|1)

symmetry 1. Super-analog of Reshetikhin formula

We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing

\mathfrak{gl}(2|1)

symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with

\mathfrak{gl}(1|1)

symmetry.