TY - JOUR
T1 - Integrals of motion from quantum toroidal algebras
AU - Feigin, B.
AU - Jimbo, M.
AU - Mukhin, E.
PY - 2017/10/23
Y1 - 2017/10/23
N2 - 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.
AB - 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.
KW - Bethe ansatz
KW - integrals of motion
KW - quantum toroidal algebras
KW - transfer matrices
UR - http://www.scopus.com/inward/record.url?scp=85032804430&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aa8e92
DO - 10.1088/1751-8121/aa8e92
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AN - SCOPUS:85032804430
SN - 1751-8113
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 46
M1 - 464001
ER -