A5048946934- Nonlinear Waves and Solitons
- Algebraic structures and combinatorial models
- Advanced Algebra and Geometry
- Advanced Topics in Algebra
- Black Holes and Theoretical Physics
- Nonlinear Photonic Systems
- Quantum chaos and dynamical systems
- Algebraic Geometry and Number Theory
- Homotopy and Cohomology in Algebraic Topology
- advanced mathematical theories
- Geometry and complex manifolds
- Mathematical functions and polynomials
- Molecular spectroscopy and chirality
- Advanced Mathematical Physics Problems
- Differential Equations and Boundary Problems
- Noncommutative and Quantum Gravity Theories
- Advanced Combinatorial Mathematics
- Advanced Operator Algebra Research
- Advanced Differential Equations and Dynamical Systems
- Advanced Mathematical Identities
- Differential Equations and Numerical Methods
- Quantum Mechanics and Non-Hermitian Physics
- Cosmology and Gravitation Theories
- Algebraic and Geometric Analysis
- Matrix Theory and Algorithms
Institute for Information Transmission Problems
2015-2024
Kurchatov Institute
2017-2024
Institute for Theoretical and Experimental Physics
2012-2022
Moscow Institute of Physics and Technology
2014-2021
Moscow Power Engineering Institute
2021
Moscow Aviation Institute
2021
National Research University Higher School of Economics
2014
Steklov Mathematical Institute
2014
Nankai University
2009
Max Planck Institute for Mathematics
1999-2006
The free field representation or "bosonization" rule 1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, quadratic in the fields. In this way, all known formulae conformal blocks correlators may be easily reproduced as certain linear combinations of these Generalization to on Riemann surfaces straightforward. However, projection rules spirit Ref. 2 are not specified. special role...
We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\Sigma_\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes elements second cohomology group $H^2(\Sigma_\tau,{\mathcal Z}(G))$, where ${\mathcal Z}(G)$ is center $G$. For any complex simple Lie $G$ and arbitrary class we define moduli space bundles, in this way construct monodromy preserving equations Hamiltonian...
We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum R-matrix. They have two parameters. The limit first one brings model to ordinary KZ equation. Another is τ. At level classical mechanics parameter τ allows extend previously obtained modified Gaudin models Schlesinger systems. Next, we notice that identities underlying generic (elliptic) KZB follow from some additional relations for properly...
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms quantum $R$-matrices. Here study simplest case -- 11-vertex $R$-matrix and related ${\rm gl}_2$ rational models. The corresponding top is equivalent to 2-body Ruijsenaars-Schneider (RS) or Calogero-Moser (CM) model depending on its description. We give different descriptions use them as building blocks for more complicated systems such Gaudin models spin chains (periodic with...
This paper is a continuation of our previous \cite{LOSZ}. For simple complex Lie groups with non-trivial center, i.e. classical simply-connected groups, $E_6$ and $E_7$ we consider elliptic Modified Calogero-Moser systems corresponding to the Higgs bundles an arbitrary characteristic class. These are generalization (CM) related contain CM some (unbroken) subalgebras. all algebras construct special basis, classes, explicit forms Lax operators Hamiltonians.
We discuss quantum dynamical elliptic R-matrices related to arbitrary complex simple Lie group G. They generalize the known vertex and play an intermediate role between these two types. The are defined by corresponding characteristic classes describing underlying vector bundles. latter elements of center Z(G) While bundles with trivial classes, Baxter-Belavin-Drinfeld-Sklyanin R-matrix corresponds generator Z_N SL(N). construct SL(N)- class explicitly IRF models.