4.6 Article

Lax equations for relativistic GL(NM,C) Gaudin models on elliptic curve

Related references

Note: Only part of the references are listed.
Article Mathematics

Lax matrices from antidominantly shifted Yangians and quantum affine algebras: A-type

Rouven Frassek et al.

Summary: In this article, we construct a family of GL(n) rational and trigonometric Lax matrices T-D(z) parametrized by Lambda(+)-valued divisors D. Our study involves the shifted Drinfeld Yangians and quantum affine algebras, showcasing a new conceptual proof and establishing a close relation between linear Lax matrices and Gelfand-Tsetlin formulas.

ADVANCES IN MATHEMATICS (2022)

Article Physics, Multidisciplinary

Higher Rank 1+1 Integrable Landau-Lifshitz Field Theories From Associative Yang-Baxter Equation

K. Atalikov et al.

Summary: We propose a construction of 1 + 1 integrable Heisenberg-Landau-Lifshitz type equations in the gl(N) case, where the dynamical variables are matrix elements of N x N matrix S with specific properties. The Lax pair with spectral parameter is constructed using a quantum R-matrix satisfying the associative Yang-Baxter equation. Equations of motion for gl(N) Landau-Lifshitz model are derived and the model is simplified in certain cases. The described family of models includes the elliptic model coming from GL(N) Baxter-Belavin elliptic R-matrix, and the well-known Sklyanin's elliptic Lax pair for XYZ Landau-Lifshitz equation is reproduced in the N = 2 case.

JETP LETTERS (2022)

Article Physics, Particles & Fields

2D Integrable systems, 4D Chern-Simons theory and affine Higgs bundles

A. Levin et al.

Summary: This article compares the construction of 2D integrable models through two gauge field theories: the 4D Chern-Simons theory and the 2D generalization of Hitchin integrable systems constructed by means of affine Higgs bundles.

EUROPEAN PHYSICAL JOURNAL C (2022)

Article Physics, Particles & Fields

Field analogue of the Ruijsenaars-Schneider model

A. Zabrodin et al.

Summary: This article proposes a field extension of the classical elliptic Ruijsenaars-Schneider model and defines and derives it through two different methods. The first method defines the model through the trace of the L-matrix, resulting in a lattice field analogue. The second method defines the model through the investigation of elliptic families of solutions to the 2D Toda equation and proves that their equations of motion are Hamiltonian. The models obtained from these two methods are equivalent.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Article Physics, Multidisciplinary

Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin

M. Fairon et al.

Summary: This study investigates the trigonometric real form of the spin Ruijsenaars-Schneider system introduced by Krichever and Zabrodin in 1995, at the level of equations of motion. The results show that the reduced system derived from Hamiltonian reduction of the 'free' system carried by a spin extension of the Heisenberg double of the U(n) Poisson-Lie group exhibits the Hamiltonian structure of the trigonometric spin Ruijsenaars-Schneider system and proves its degenerate integrability.

ANNALES HENRI POINCARE (2021)

Article Physics, Mathematical

A decoupling property of some Poisson structures on Matnxd(C)xMatdxn(C) supporting GL(n,C)xGL(d,C) Poisson-Lie symmetry

M. Fairon et al.

Summary: The research focuses on a holomorphic Poisson structure defined on a linear space, which is covariant under the left actions of standard Poisson-Lie groups. The Poisson brackets of the matrix elements contain quadratic and constant terms, and the Poisson tensor is non-degenerate on a dense subset. The study also includes constructing a local Poisson map from independent copies of a specific linear space into another, which is a holomorphic diffeomorphism in a neighborhood of 0.

JOURNAL OF MATHEMATICAL PHYSICS (2021)

Article Mathematics, Applied

Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations

K. Atalikov et al.

Summary: This paper discusses the continuous version of the classical IRF-Vertex relation in the context of the Calogero-Moser-Sutherland models. The study is based on constructing modifications of infinite rank Higgs bundles over elliptic curves and their degenerations, and describes the previously predicted gauge equivalence between L-A pairs of Landau-Lifshitz type equations and 1 + 1 field theory generalization of the Calogero-Moser-Sutherland models. The sl(2) case is specifically studied, with explicit changes of variables obtained between rational, trigonometric, and elliptic models.

JOURNAL OF GEOMETRY AND PHYSICS (2021)

Article Physics, Multidisciplinary

QUADRATIC ALGEBRAS BASED ON SL(NM) ELLIPTIC QUANTUM R-MATRICES

I. A. Sechin et al.

Summary: In this study, a quadratic quantum algebra is constructed based on the dynamical RLL-relation for the quantum R-matrix associated with SL(NM)-bundles with a nontrivial characteristic class over an elliptic curve. This R-matrix generalizes existing matrices and the obtained quadratic relations provide a new set of relationships.

THEORETICAL AND MATHEMATICAL PHYSICS (2021)

Article Physics, Mathematical

On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system

Oleg Chalykh et al.

LETTERS IN MATHEMATICAL PHYSICS (2020)

Article Physics, Multidisciplinary

Trigonometric Integrable Tops from Solutions of Associative Yang-Baxter Equation

T. Krasnov et al.

ANNALES HENRI POINCARE (2019)

Article Mathematics, Applied

Multiplicative Hitchin systems and supersymmetric gauge theory

Chris Elliott et al.

SELECTA MATHEMATICA-NEW SERIES (2019)

Article Physics, Particles & Fields

Poisson-Lie analogues of spin Sutherland models

L. Feher

NUCLEAR PHYSICS B (2019)

Article Physics, Multidisciplinary

Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation

A. Levin et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2016)

Article Physics, Particles & Fields

Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings

A. Mironov et al.

JOURNAL OF HIGH ENERGY PHYSICS (2016)

Article Physics, Multidisciplinary

QUANTUM BAXTER-BELAVIN R-MATRICES AND MULTIDIMENSIONAL LAX PAIRS FOR PAINLEVE VI

A. M. Levin et al.

THEORETICAL AND MATHEMATICAL PHYSICS (2015)

Article Physics, Multidisciplinary

On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants

N. Delice et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2015)

Article Physics, Multidisciplinary

Characteristic classes of SL(N, C)-bundles and quantum dynamical elliptic R-matrices

A. Levin et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2013)

Article Physics, Multidisciplinary

Modifications of bundles, elliptic integrable systems, and related problems

A. V. Zotov et al.

THEORETICAL AND MATHEMATICAL PHYSICS (2013)

Article Physics, Mathematical

Characteristic Classes and Hitchin Systems. General Construction

A. Levin et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2012)

Article Mathematics, Applied

Calogero-Moser systems for simple Lie groups and characteristic classes of bundles

A. Levin et al.

JOURNAL OF GEOMETRY AND PHYSICS (2012)

Article Physics, Mathematical

1+1 Gaudin Model

Andrei V. Zotov

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS (2011)

Article Physics, Multidisciplinary

Quadratic algebras related to elliptic curves

A. V. Zotov et al.

THEORETICAL AND MATHEMATICAL PHYSICS (2008)

Article Physics, Mathematical

Bihamiltonian structures and quadratic algebras in hydrodynamics and on non-commutative torus

B Khesin et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2004)

Article Physics, Multidisciplinary

Classical r-matrices and the Feigin-Odesskii algebra via Hamiltonian and Poisson reductions

HW Braden et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2003)

Article Physics, Mathematical

Hitchin systems - Symplectic Hecke correspondence and two-dimensional version

AM Levin et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2003)

Article Physics, Mathematical

Vector bundles and lax equations on algebraic curves

I Krichever

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2002)

Article Mathematics

Classical Yang-Baxter equation and the A∞-constraint

A Polishchuk

ADVANCES IN MATHEMATICS (2002)