  The action of $Sp(3)$ on a vector space $V_3\in \mathbb H^3$ is analyzed. The
transitive action of the group is conveyed by the flag manifold (coset space)
$Sp(3)/Sp(1)^3\sim G/H$, a Wallach space. The curvature two-forms are shown to
mediate pair-wise interactions between the components of the $\mathbb H^3$
vector space. The root space of the flag manifold is shown to be isomorphic to
that of $SU(3)$, suggesting similarities between the representations of the
flag manifold and those of $SU(3)$. The passage from $SU(3)$ to $Sp(3)$ and the
interpretation given here encompasses the spin of the fermionic components of
$V_3$. Composite fermions are representable as linear combinations of product
states of the eigenvectors of $G/H$.
