Consider a system described by the quasispin model of Problem 31.3 for $G>0$ with two identical fermions in a single $j$-shell. Show that the allowed seniorities are $v=0,2$, the allowed angular momenta are $J=0,2, \ldots, 2 j-1$, and that

\[\begin{array}{ll}v=2 & \\v=0 & J=2,4, \ldots, 2 j-1 \\& J=0\end{array}\]

is the schematic form of the spectrum.