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arXiv · 0810.3131

Generating Series for Nested Bethe Vectors

Sergey Khoroshkin·Stanislav Pakuliak
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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 $U_q(\widehat{\mathfrak{gl}}_2)$.

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BibTeXRIS

Sergey Khoroshkin, Stanislav Pakuliak. 2008-11-24. Generating Series for Nested Bethe Vectors. https://doi.org/10.3842/sigma.2008.081

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