  We study emergent behaviors of the Lohe hermitian sphere(LHS) model which is
an aggregation model on ${\mathbb C}^d$. The LHS model is a complex analog of
the Lohe sphere model on ${\mathbb R}^d$, and hermitian spheres are invariant
sets for the LHS dynamics. For the derivation of the LHS model, we use a
top-down approach, namely a reduction from a high-rank aggregation model,
"$\textit{the Lohe tensor model}$." The Lohe tensor model is a first-order
aggregation model on the space of tensors with the same rank and sizes, and it
was first proposed by the authors in a recent work \cite{H-P}. In this work, we
study how the LHS model appears as a special case of the Lohe tensor model and
for the proposed model, we provide a cross-ratio like conserved quantity, a
sufficient framework for the complete aggregation and a uniform
$\ell^p$-stability estimate with respect to initial data.
