Dmitry V. Talalaev

Universal R-matrix formalism for the spin Calogero-Moser system and its difference counterpart

The expression of the quantum Ruijsenaars-Schneider Hamiltonian is obtained in the framework of the dynamical

Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of 2d Quantum Integrable Systems

R

Hitchin systems on singular curves II. Gluing subschemes.

-matrix formalism. This generalizes to the case of

Cohomologies of n-simplex relations

U_q(sl_n)

On the Lie-formality of Poisson manifolds

the result obtained by O. Babelon, D. Bernard and E. Billey for

Drinfeld-Sokolov reduction in quantum algebras

U_q(sl_2)

Cohomology of the tetrahedral complex and quasi-invariants of 2-knots

which is the higher difference Lame operator. The general method involved is the universal

Asymmetric Hopfield neural network and twisted tetrahedron equation.

R

Towards integrable structure in 3d Ising model

-matrix construction.

Drinfeld–Sokolov reduction in quantum algebras: canonical form of generating matrices

The main aim of this work is to develop a method of constructing higher Hamiltonians of quantum integrable systems associated with the solution of the Zamolodchikov tetrahedral equation. As opposed to the result of V.V. Bazhanov and S.M. Sergeev the approach presented here is effective for generic solutions of the tetrahedral equation without spectral parameter. In a sense, this result is a two-dimensional generalization of the method by J.-M. Maillet. The work is a part of the project relating the tetrahedral equation with the quasi-invariants of 2-knots.