On tensor products of representations of the non-standard q-deformed algebra U-q '(so(n))

The tensor product of vector and arbitrary representations of the non-stand ard q-deformation U'(q) (so(n)) of the universal enveloping algebra U (so(n )) of Lie algebra so(n) is defined. The Clebsch-Gordan coefficients of the tensor product of vector and arbitrary classical type representations of q- algebra U'(q)(so(n)) are found in an explicit form. Some important corollar ies are considered. In particular, the Wigner-Eckart theorem for vector ope rators is proved.