  Using observations in the COSMOS field, we report an intriguing correlation
between the star formation activity of massive (~10^{11.4}\msol) central
galaxies, their stellar masses, and the large-scale (~10 Mpc) environments of
their group-mass (~10^{13.6}\msol) dark matter halos. Probing the redshift
range z=[0.2,1.0], our measurements come from two independent sources: an X-ray
detected group catalog and constraints on the stellar-to-halo mass relation
derived from a combination of clustering and weak lensing statistics. At z=1,
we find that the stellar mass in star-forming centrals is a factor of two less
than in passive centrals at the same halo mass. This implies that the presence
or lack of star formation in group-scale centrals cannot be a stochastic
process. By z=0, the offset reverses, probably as a result of the different
growth rates of these objects. A similar but weaker trend is observed when
dividing the sample by morphology rather than star formation. Remarkably, we
find that star-forming centrals at z~1 live in groups that are significantly
more clustered on 10 Mpc scales than similar mass groups hosting passive
centrals. We discuss this signal in the context of halo assembly and recent
simulations, suggesting that star-forming centrals prefer halos with higher
angular momentum and/or formation histories with more recent growth; such halos
are known to evolve in denser large-scale environments. If confirmed, this
would be evidence of an early established link between the assembly history of
halos on large scales and the future properties of the galaxies that form
inside them.
