Browsing by Subject "quantum toroidal algebras"

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    Integrals of motion from quantum toroidal algebras
    (IOP, 2017) Feigin, B.; Jimbo, M.; Mukhin, Eugene; Mathematical Sciences, School of Science
    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 $({\mathfrak {gl}}_m, {\mathfrak {gl}}_n)$ 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 ${\mathfrak{sl}}_2$ .
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    Quantum Toroidal Comodule Algebra of Type A(n-1) and Integrals of Motion
    (Foundation Compositio Mathematica, 2022-07-07) Feigin, Boris; Jimbo, Michio; Mukhin, Evgeny; Mathematical Sciences, School of Science
    We introduce an algebra Kn which has a structure of a left comodule over the quantum toroidal algebra of type An−1. Algebra Kn is a higher rank generalization of K1, which provides a uniform description of deformed W algebras associated with Lie (super)algebras of types BCD. We show that Kn possesses a family of commutative subalgebras.