Integrals of motion from quantum toroidal algebras

B. Feigin, M. Jimbo, E. Mukhin

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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 (glm, gln) 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 sl2.

Original languageEnglish
Article number464001
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number46
DOIs
StatePublished - 23 Oct 2017
Externally publishedYes

Keywords

  • Bethe ansatz
  • integrals of motion
  • quantum toroidal algebras
  • transfer matrices

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