Angular momentum algebra, Wigner-Eckart theorem

Another very useful expression is the case where the operators act in just one space. We state here without showing that the reduced matrix element $$ \langle j_a||W^{r}||j_b\rangle=\langle j_a||\left[T^p\times T^q\right]^{r}||j_b\rangle= (-1)^{j_a+j_b+r}\sqrt{2r+1} \sum_{j_c}\begin{Bmatrix} j_b & j_a & r\\ p & q & j_c \end{Bmatrix} $$ $$ \times \langle j_a||T^p||j_c\rangle \langle j_c||T^q||j_b\rangle. $$