Integrals of motion from quantum toroidal algebras
Quantum Algebra
2017-11-22 v2 Mathematical Physics
math.MP
Abstract
We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model. We also discuss the (gl(m),gl(n)) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine sl(2).
Cite
@article{arxiv.1705.07984,
title = {Integrals of motion from quantum toroidal algebras},
author = {B. Feigin and M. Jimbo and E. Mukhin},
journal= {arXiv preprint arXiv:1705.07984},
year = {2017}
}
Comments
Latex, 28 pages, minor revision, some misprints corrected