26 citations · 187 across the 16 of their papers we have counts for
17 papers
Dualities in quantum integrable many-body systems and integrable probabilities -- I
A. Gorsky, M. Vasilyev, A. Zotov
In this study we map the dualities observed in the framework of integrable probabilities into the dualities familiar in a realm of integrable many-body systems. The dualities betwe…
Multi-pole extension for elliptic models of interacting integrable tops
E. Trunina, A. Zotov
We review and give detailed description for Gaudin models related to holomorphic vector bundles of rank and degree over elliptic curve with punctures.…
Quadratic algebras based on SL(NM) elliptic quantum R-matrices
I. A. Sechin, A. V. Zotov
We construct quadratic quantum algebra based on the dynamical RLL-relation for the quantum -matrix related to -bundles with nontrivial characteristic class over elliptic…
Odd supersymmetric Kronecker elliptic function and Yang-Baxter equations
A. Levin, M. Olshanetsky, A. Zotov
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an applic…
GL(NM) quantum dynamical -matrix based on solution of the associative Yang-Baxter equation
I. Sechin, A. Zotov
In this letter we construct -valued dynamical -matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental repre…
Generalized model of interacting integrable tops
A. Grekov, I. Sechin, A. Zotov
We introduce a family of classical integrable systems describing dynamics of interacting integrable tops. It extends the previously known model of interacting elli…
Trigonometric integrable tops from solutions of associative Yang-Baxter equation
T. Krasnov, A. Zotov
We consider a special class of quantum non-dynamical -matrices in the fundamental representation of with spectral parameter given by trigonometric solutions of the…
Supersymmetric extension of qKZ-Ruijsenaars correspondence
A. Grekov, A. Zabrodin, A. Zotov
We describe the correspondence of the Matsuo-Cherednik type between the quantum -body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to sup…
On factorized Lax pairs for classical many-body integrable systems
M. Vasilyev, A. Zotov
In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss…
On R-matrix valued Lax pairs for Calogero-Moser models
A. Grekov, A. Zotov
The article is devoted to the study of -matrix-valued Lax pairs for -body (elliptic) Calogero-Moser models. Their matrix elements are given by quantum $…
Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian
A. Zabrodin, A. Zotov
We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) Ruijsenaars-Schneider model. It is based on the first order equations…
Relativistic elliptic matrix tops and finite Fourier transformations
A. Zotov
We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the "o…
QKZ-Ruijsenaars correspondence revisited
A. Zabrodin, A. Zotov
We discuss the Matsuo-Cherednik type correspondence between the quantum Knizhnik-Zamolodchikov equations associated with and the -particle quantum Ruijsenaars model, wit…
KZ-Calogero correspondence revisited
A. Zabrodin, A. Zotov
We discuss the correspondence between the Knizhnik-Zamolodchikov equations associated with and the -particle quantum Calogero model in the case when is not necessari…
Asymmetric 6-vertex model and classical Ruijsenaars-Schneider system of particles
A. Liashyk, D. Rudneva, A. Zabrodin +1
We discuss the correspondence between models solved by Bethe ansatz and classical integrable systems of Calogero type. We illustrate the correspondence by the simplest example of t…
Trigonometric version of quantum-classical duality in integrable systems
M. Beketov, A. Liashyk, A. Zabrodin +1
We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsena…
Classical-Quantum Correspondence and Functional Relations for Painleve Equations
A. Zabrodin, A. Zotov
In the light of the Quantum Painleve-Calogero Correspondence established in our previous papers [1,2], we investigate the inverse problem. We imply that this type of the correspond…