Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 081, 23 pages      arXiv:0810.3131      https://doi.org/10.3842/SIGMA.2008.081
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Generating Series for Nested Bethe Vectors

Sergey Khoroshkin a and Stanislav Pakuliak b, a
a) Institute of Theoretical & Experimental Physics, 117259 Moscow, Russia
b) Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia

Received September 14, 2008; Published online November 24, 2008

Abstract
We reformulate nested relations between off-shell Uq(^glN) Bethe vectors as a certain equation on generating series of strings of the composed Uq(^glN) 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 Uq(^gl2).

Key words: Bethe ansatz; current algebras; quantum integrable models.

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