English

Generating Series for Nested Bethe Vectors

Quantum Algebra 2008-11-24 v2 Mathematical Physics math.MP

Abstract

We reformulate nested relations between off-shell Uq(gl^N)U_q(\widehat{\mathfrak{gl}}_N) Bethe vectors as a certain equation on generating series of strings of the composed Uq(gl^N)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 Poincar\'e 7 (2006), 1217-1268, math-ph/0512037] for the parameters of universal Bethe vectors of the algebra Uq(gl^2)U_q(\widehat{\mathfrak{gl}}_2).

Cite

@article{arxiv.0810.3131,
  title  = {Generating Series for Nested Bethe Vectors},
  author = {Sergey Khoroshkin and Stanislav Pakuliak},
  journal= {arXiv preprint arXiv:0810.3131},
  year   = {2008}
}

Comments

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/

R2 v1 2026-06-21T11:31:57.795Z