English

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).

Keywords

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

R2 v1 2026-06-22T19:55:26.813Z