By construction $SU(2)$ is contained in $U(2)$, the special unitary and unitary groups respectively. Thus, any representation of $U(2)$ will induce a representation of $SU(2)$. The irreducible irreps of $SU(2)$ are labeled by ${\bf N_0}$, and the irreps of $U(2)$ are labelled by $2$ integers. For $(n_1,n_2)$ an irrep of $U(2)$, what is the natural number corresponding to the restricted irrep of $SU(2)$.
I am also interested in the analogous question for $SU(3)$ branched by $U(2)$.