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Generating series for nested Bethe vectors. (English) Zbl 1215.17011

Summary: 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 [D. Arnaudon et al., Ann. Henri Poincaré 7, No. 7-8, 1217–1268 (2006; Zbl 1115.82005), see also arXiv:math-ph/0512037] for the parameters of universal Bethe vectors of the algebra \(U_q(\widehat {\mathfrak{gl}}_2)\).

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R12 Groups and algebras in quantum theory and relations with integrable systems
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory

Citations:

Zbl 1115.82005
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