arXiv subjects
Publications and source records attributed to M. A. Sokolov.
The generating function of the second kind bivariate Chebyshev polynomials associated with the simple Lie algebra $G_2$ is constructed by the method proposed in \cite{DKS} and \cite{DKS1}.
We propose a new method of calculation of generating functions of Chebyshev polynomials in several variables associated with root systems of simple Lie algebras. We obtain the generating functions of the polynomials in two variables corresponding to the Lie algebras C_2 and G_2.
In this paper generating functions of three variables Chebyshev polynomials associated with the root system of $A_3$ Lie algebra are obtained.
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
This work is concerned with a quantization of the Pais-Uhlenbeck oscillators from the point of view of their multi-Hamiltonian structures. It is shown that the 2n-th order oscillator with a simple spectrum is equivalent to the usual anisotropic n - dimensional oscillator.
Some examples are given of finite dimensional Lie bialgebras whose brackets and cobrackets are determined by pairs of $r$-matrices.
It is shown that the properties of the Gauss decomposition of quantum groups and the known Jimbo homomorphism permit us to realize these groups as subalgebras of well defined algebras constructed from generators of the corresponding undeformed Lie algebras.
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality aspects of the Gauss decomposition are also touched. For clarity of exposition a few simple examples are considered in some details.
The Gauss decompositions of the quantum groups, related to classical Lie groups and supergroups are considered by the elementary algebraic and $R$-matrix methods. The commutation relations between new basis generators (which are introduced by the decomposition) are described in some details. It is shown that the reduction of the independent generator number in the new basis to the dimension of related classical (super) group is possible. The classical expression for (super) determinant through the Gauss decomposition generators is not changed in the deformed case. The symplectic quantum group $Sp_q(2)$ and supergroups $GL_q(1|1), GL_q(2|1)$ are considered as examples.
The new method of q-bosonization for quantum groups based on the Gauss decomposition of a transfer matrix of generators is suggested. The simplest example of the quantum group $GL_q(2)$ is considered in some details.
In this letter some properties of the Gauss decomposition of quantum group $GL_q(n)$ with application to q-bosonization are considered.