On tensor products of representations of the non-standardq-deformed algebraU'q(son)

Abstract

The tensor product of vector and arbitrary representations of the non-standard q-deformation U'q(son) of the universal enveloping algebra U(son) of Lie algebra son is defined. The Clebsch-Gordan coefficients of the tensor product of vector and arbitrary classical type representations of q-algebra U'q(son) are found in an explicit form. Some important corollaries are considered. In particular, the Wigner-Eckart theorem for vector operators is proved.