  The clustering of dark matter halos depends on the assembly history of halos
at fixed halo mass; a phenomenon referred to as \textit{halo assembly bias}.
Halo assembly bias is readily observed in cosmological simulations of dark
matter. However, it is difficult to detect it in observations. The
identification of galaxy or cluster properties correlated with the formation
time of the halo at fixed halo mass and the ability to select galaxy clusters
free from projection effects are the two most significant hurdles in the
observational detection of halo assembly bias. The latter, in particular, can
cause a misleading detection of halo assembly bias by boosting the amplitude of
lensing and clustering on large scales. This study uses twelve different
properties of central galaxies of SDSS redMaPPer clusters derived from
spectroscopy to divide the clusters into sub-samples. We test the dependence of
the clustering amplitude on these properties at fixed richness. We first infer
halo mass and bias using weak lensing signals around the clusters using shapes
of galaxies from the SDSS survey. We validate the bias difference between the
two subsamples using cluster-galaxy cross-correlations. This methodology allows
us to decouple the contamination due to the projection effects from the halo
assembly bias signals. We do not find any significant evidence of a difference
in the clustering amplitudes correlated with any of our explored properties.
Our results indicate that central galaxy properties may not correlate
significantly with the halo assembly histories at fixed richness.
