102 citations · 621 across the 36 of their papers we have counts for
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Classification theorem on irreducible representations of the q-deformed algebra U'_q(so(n))
N. Z. Iorgov, A. U. Klimyk
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide w…
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…
On the Casimir Elements of q-Algebras U'_q(so_n) and Their Eigenvalues in Representations
A. M. Gavrilik, N. Z. Iorgov
The nonstandard q-deformed algebras U'_q(so_n) are known to possess q-analogues of Gel'fand-Tsetlin type representations. For these q-algebras, all the Casimir elements (correspond…
Nonclassical type representations of the q-deformed algebra
N. Z. Iorgov, A. U. Klimyk
The nonstandard q-deformation of the universal enveloping algebra has irreducible finite dimensional representations which are a q-deformation of…
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})…