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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…
A q-analogue of the Wigner-Eckart theorem for the nonstandard q-deformed algebra U'_q(so(n))
N. Z. Iorgov
The tensor product of vector and arbitrary representations of the nonstandard q-deformation U'_q(so(n)) of the universal enveloping algebra U(so(n)) of Lie algebra so(n) is defined…
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…
Nonclassical representations of the nonstandard deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1})
N. Z. Iorgov, A. U. Klimyk
The aim of this paper is to announce the results on irreducible nonclassical type representations of the nonstandard q-deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1}) of the…
Representations of quantum algebra U_q(u_{n,1})
V. A. Groza, N. Z. Iorgov, A. U. Klimyk
Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1})…