= Rotation content of induced Lorentz representations
{title2=$\bigoplus_{j=|n|/2,\ |n|/2+1,\ldots}V_j$}
In the compact picture of a principal-series <group representation> of the <Lorentz spinor double cover>, functions on <SU(2)> have a fixed right-torus character $e^{-in\vartheta}$. Expanding into spin matrix coefficients leaves one right weight in each allowed spin, giving the displayed multiplicity-one rotation decomposition. The boost action couples these spaces. The central element acts by $(-1)^n$; even $n$ yields integer rotation spins and a <group representation> of the connected Lorentz group.
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