15 citations · 16 across the 4 of their papers we have counts for
7 papers
Duality of q-polynomials, orthogonal on countable sets of points
N. M. Atakishiyev, A. U. Klimyk
We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jac…
On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
N. M. Atakishiyev, A. U. Klimyk
This paper studies properties of q-Jacobi polynomials and their duals by means of operators of the discrete series representations for the quantum algebra U_q(su_{1,1}). Spectrum a…
Hamiltonian Type Operators in Representations of the Quantum Algebra U_q(su_{1,1})
N. M. Atakishiyev, A. U. Klimyk
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical syste…
Harmonics on the Quantum Euclidean Space Related to the Quantum Orthogonal Group
N. Z. Iorgov, A. U. Klimyk
The aim of this paper is to study harmonic polynomials on the quantum Euclidean space E^N_q generated by elements x_i, i=1,2,...,N, on which the quantum group SO_q(N) acts. The har…
Classification of irreducible representations of the q-deformed algebra U'_q(so_n)
A. U. Klimyk
A classification of finite dimensional irreducible representations of the nonstandard -deformation of the universal enveloping algebra of the Lie alge…
The Nonstandard Deformation U'_q(so_n) For q a Root of Unity
N. Z. Iorgov, A. U. Klimyk
We describe properties of the nonstandard q-deformation U'_q(so_n) of the universal enveloping algebra U(so_n) of the Lie algebra so_n which does not coincide with the Drinfeld--Ji…