  The existence of states with angular momenta $I = 4$ and~6 of four fermions
in an angular momentum $j = 9/2$ shell that are stationary for any rotationally
invariant two-body interaction despite the presence of other states with the
same angular momentum, the Escuderos-Zamick states, is shown to be equivalent
to the invariance to any such interaction of the span of states generated from
$I = 0$ states by one-body operators. This invariance is verified by exact
calculation independently of previous verifications of the equivalent
statement. It explains the occurrence of the Escuderos-Zamick states for just
$I = 4$ and 6. The action of an arbitrary interaction on the invariant space
and its orthogonal complement is analyzed, leading to a relation of the
Escuderos-Zamick energy levels to levels with $I = 10$ and 12. Aspects of the
observed spectra of $^{94}$Ru, $^{96}$Pd, and $^{74}$Ni are discussed in the
light of this relation.
