  Let $A$ be a commutative algebra equipped with an action of a group $G$. The
so-called $G$-primes of $A$ are the equivariant analogs of prime ideals, and of
central importance in equivariant commutative algebra. When $G$ is an infinite
dimensional group, these ideals can be very subtle: for instance, distinct
$G$-primes can have the same radical. In previous work, the second author
showed that if $G$ is ${\bf GL}$ and $A$ is a polynomial representation, then
these pathologies disappear when working with super vector spaces; this leads
to a geometric description of $G$-primes of $A$. In the present paper, we
construct an abstract framework around this result, and apply the framework to
prove analogous results for other (super)groups. We give some applications to
the queer determinantal ideals.
