A bstract We describe classical top-like integrable systems arising from the quantum
exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in …

A bstract We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB)
equations with Ñ punctures by deformation of the corresponding quantum gl N rational R …

A bstract In this paper we clarify the relationship between inhomogeneous quantum spin
chains and classical integrable many-body systems. It provides an alternative (to the nested …

Abstract A (q, t)-deformation of the 2d Toda integrable hierarchy is introduced by enhancing
the underlying symmetry algebra gl^(∞)≃ qW 1+∞ to the quantum toroidal gl (1) algebra …

This paper is intended to serve as a review of a series of papers with Nikita Nekrasov, where
we achieved several important results concerning the relation between the moduli space of …

We extend the quantum–classical duality to the trigonometric (hyperbolic) case. The duality
establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars …

We find all formal solutions to the ℏ-dependent KP hierarchy. They are characterized by
certain Cauchy-like data. The solutions are found in the form of formal series for the tau …

A bstract For integrable inhomogeneous supersymmetric spin chains (generalized graded
magnets) constructed employing Y (gl (N| M))-invariant R-matrices in finite-dimensional …

Beta-ensembles of random matrices are naturally considered as quantum integrable
systems, in particular, due to their relation with conformal field theory, and more recently …

We discuss the correspondence between the Knizhnik–Zamolodchikov equations
associated with GL (N) and the n-particle quantum Calogero model in the case when n is not …