International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 2, Pages 225-262

Classification theorem on irreducible representations of the q-deformed algebra Uq(son)

N. Z. Iorgov and A. U. Klimyk

Mathematical Methods in Theoretical Physics Department, Bogolyubov Institute for Theoretical Physics, Metrologichna Street, Kiev 03143, Ukraine

Received 8 August 2004

Copyright © 2005 N. Z. Iorgov and A. U. Klimyk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation Uq(son) (which does not coincide with the Drinfel'd-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son()) of the Lie algebra son() when q is not a root of unity. These representations are exhausted by irreducible representations of the classical type and of the nonclassical type. The theorem on complete reducibility of finite-dimensional representations of Uq(son) is proved.