  The antisymmetrized geminal power (AGP) wavefunction has a long history and
is known by different names in various chemical and physical problems. There
has been recent interest in using AGP as a starting point for strongly
correlated electrons. Here, we show that in a seniority-conserving regime,
different AGP based correlator representations based on generators of the
algebra, killing operators, and geminal replacement operators are all
equivalent. We implement one representation that uses number operators as
correlators and has linearly independent curvilinear metrics to distinguish the
regions of Hilbert space. This correlation method called J-CI, provides
excellent accuracy in energies when applied to the pairing Hamiltonian.
