Abstract: The generalized coupling coefficients of group chains (Ⅰ) and (Ⅲ) were firstly discussed, and then generalized Wigner-Eckart theorem of coupling tensor operators of group chains (Ⅰ) and (Ⅲ) were investigated. We have gained the general expression of reduced matrix element of coupling tensor operators in the third section. As an example, the matrix element of Majorana operator was calculated in the last section. The results shows it is consistent with the result from the literature.

Key words: Coupling coefficients, Coupling tensor operator, Wigner-Eckart theorem