= Representations of SO(4) from two SU2 spins
{title2=$(j_L,j_R),\quad j_L+j_R\in\mathbb Z$}
Tensor products $V_{j_L}\otimes V_{j_R}$ give the <irreducible representations> of the <Spin(4) double cover>. The simultaneous central sign acts by $(-1)^{2j_L+2j_R}$, so exactly the integer-sum pairs descend to <SO(4)>. Their dimensions are $(2j_L+1)(2j_R+1)$. Under the diagonal spatial rotation subgroup, the <Clebsch-Gordan decomposition for SU2> gives spins from $|j_L-j_R|$ through $j_L+j_R$ in steps of one.
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