Khoroshkin, Sergey; Pakuliak, Stanislav [Pakulyak, S. Z.] Generating series for nested Bethe vectors. (English) Zbl 1215.17011 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 081, 23 p. (2008). 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 Keywords:Bethe ansatz; current algebras; quantum integrable models Citations:Zbl 1115.82005 PDFBibTeX XMLCite \textit{S. Khoroshkin} and \textit{S. Pakuliak}, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 081, 23 p. (2008; Zbl 1215.17011) Full Text: DOI arXiv EuDML