  Based on the DECaLS shear catalog, we study the scaling relations between
halo mass($M_{\rm h}$) and various proxies for SDSS central galaxies, including
stellar mass($M_*$), stellar velocity dispersion($\sigma_*$), abundance
matching halo mass($M_{\rm AM}$) and satellite velocity dispersion($\sigma_{\rm
s}$), and their dependencies on galaxy and group properties. In general, these
proxies all have strong positive correlations with $M_{\rm h}$, consistent with
previous studies. We find that the $M_{\rm h}$-$M_*$ and $M_{\rm h}$-$\sigma_*$
relations depend strongly on group richness($N_{\rm sat}$), while the $M_{\rm
h}$-$M_{\rm AM}$ and $M_{\rm h}$-$\sigma_{\rm s}$ relations are independent of
it. Moreover, the dependence on star formation rate(SFR) is rather weak in the
$M_{\rm h}$-$\sigma_*$ and $M_{\rm h}$-$\sigma_{\rm s}$ relations, but very
prominent in the other two. $\sigma_{\rm s}$ is thus the best proxy among them,
and its scaling relation is in good agreement with hydro-dynamical simulations.
However, estimating $\sigma_{\rm s}$ accurately for individual groups/clusters
is challenging because of interlopers and the requirement for sufficient
satellites. We construct new proxies by combining $M_*$, $\sigma_*$, and
$M_{\rm AM}$, and find the proxy with 30\% contribution from $M_{\rm AM}$ and
70\% from $\sigma_*$ can minimize the dependence on $N_{\rm sat}$ and SFR. We
obtain the $M_{\rm h}$-supermassive black hole(SMBH) mass relation via the SMBH
scaling relation and find indications for rapid and linear growth phases for
SMBH. We also find that correlations among $M_{\rm h}$, $M_*$ and $\sigma_*$
change with $M_*$, indicating that different processes drive the growth of
galaxies and SMBH at different stages.
