Generating Series for Nested Bethe Vectors

Abstract

We reformulate nested relations between off-shell $U_q({\widehat{\mathfrak{gl}}}_N)$ Bethe vectors as a certain equation on generating series of strings of the composed $U_q({\widehat{\mathfrak{gl}}}_N)$ currents. Using inversion of the generating series we find a new type of hierarchical relations between universal off-shell Bethe vectors, useful for a derivation of Bethe equation. As an example of application, we use these relations for a derivation of analytical Bethe ansatz equations [Arnaudon D. et al., Ann. Henri Poincaré 7 (2006), 1217-1268, math-ph/0512037] for the parameters of universal Bethe vectors of the algebra $U_q({\widehat{\mathfrak{gl}}}_2)$.

This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (4)

• Combinatorial Formulae for Nested Bethe Vectors
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Bethe Ansatz for the Universal Weight Function