Generating Series for Nested Bethe Vectors
Abstract
We reformulate nested relations between off-shell Bethe vectors as a certain equation on generating series of strings of the composed 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 .
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/