110 citations · 800 across the 39 of their papers we have counts for
37 papers
Gauge equivalence between 1+1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation
K. Atalikov, A. Zotov
In this paper we study 1+1 field generalization of the rational -body Calogero-Moser model. We show that this model is gauge equivalent to some special higher rank matrix Landau…
Higher rank generalization of 11-vertex rational R-matrix: IRF-Vertex relations and associative Yang-Baxter equation
K. Atalikov, A. Zotov
We study rational -matrix, which turns into the 11-vertex -matrix in the case. First, we describe its relations to dynamical and semi-dynamical -matrice…
On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators
M. Matushko, A. Zotov
We propose and prove a set of identities for elliptic -matrix (in the fundamental representation). In the scalar case () these are elliptic function identities…
Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
K. Atalikov, A. Zotov
We propose a construction of 1+1 integrable Heisenberg-Landau-Lifshitz type equations in the case. The dynamical variables are matrix elements of matrix $S…
Lax equations for relativistic Gaudin models on elliptic curve
E. Trunina, A. Zotov
We describe the most general classical elliptic finite-dimensional integrable system, which Lax matrix has simple poles on elliptic curve. For it reproduc…
2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles
A. Levin, M. Olshanetsky, A. Zotov
In this short review we compare constructions of 2d integrable models by means of two gauge field theories. The first one is the 4d Chern-Simons (4d-CS) theory proposed by Costello…
Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
M. Matushko, A. Zotov
We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars…
Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
M. Matushko, A. Zotov
We propose commuting set of matrix-valued difference operators in terms of the elliptic Baxter-Belavin -matrix in the fundamental representation of . In the scalar c…
Field analogue of the Ruijsenaars-Schneider model
A. Zabrodin, A. Zotov
We suggest a field extension of the classical elliptic Ruijsenaars-Schneider model. The model is defined in two different ways which lead to the same result. The first one is via t…
On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta
A. Grekov, A. Zotov
The infinite number of particles limit in the dual to elliptic Ruijsenaars model (coordinate trigonometric degeneration of quantum double elliptic model) is proposed using the Naza…
Integrable System of Generalized Relativistic Interacting Tops
I. Sechin, A. Zotov
A family of integrable models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case ), and on the other hand it gen…
Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations
K. Atalikov, A. Zotov
We give detailed description for continuous version of the classical IRF-Vertex relation, where on the IRF side we deal with the Calogero-Moser-Sutherland models. Our study is base…
Characteristic determinant and Manakov triple for the double elliptic integrable system
A. Grekov, A. Zotov
Using the intertwining matrix of the IRF-Vertex correspondence we propose a determinant representation for the generating function of the commuting Hamiltonians of the double ellip…
Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
M. Vasilyev, A. Zabrodin, A. Zotov
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras ,…
Scalar products of Bethe vectors in the 8-vertex model
N. Slavnov, A. Zabrodin, A. Zotov
We obtain a determinant representation of normalized scalar products of on-shell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational a…
Quantum-classical duality for Gaudin magnets with boundary
M. Vasilyev, A. Zabrodin, A. Zotov
We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the roo…
Odd supersymmetrization of elliptic R-matrices
A. Levin, M. Olshanetsky, A. Zotov
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construc…
Quasi-compact Higgs bundles and Calogero-Sutherland systems with two types spins
S. Kharchev, A. Levin, M. Olshanetsky +1
We define the quasi-compact Higgs -bundles over singular curves introduced in our previous paper for the Lie group SL(). The quasi-compact structure means that th…
Calogero-Sutherland system with two types interacting spins
S. Kharchev, A. Levin, M. Olshanetsky +1
We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spi…
Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation
A. Levin, M. Olshanetsky, A. Zotov
In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on -matrix description which provides Lax pairs in te…
Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations
A. Levin, M. Olshanetsky, A. Zotov
We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by a…
Yang-Baxter equations with two Planck constants
A. Levin, M. Olshanetsky, A. Zotov
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form…
Supersymmetric quantum spin chains and classical integrable systems
Zengo Tsuboi, Anton Zabrodin, Andrei Zotov
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we…
Planck Constant as Spectral Parameter in Integrable Systems and KZB Equations
A. Levin, M. Olshanetsky, A. Zotov
We construct special rational Knizhnik-Zamolodchikov-Bernard (KZB) equations with punctures by deformation of the corresponding quantum rationa…