  Let $M$ be complex projective manifold, and $A$ a positive line bundle on it.
Assume that $SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing
moment map, and that this action linearizes to $A$. Then there is an associated
unitary representation of $G$ on the associated algebro-geometric Hardy space,
and the isotypical components are all finite dimensional. We consider the local
and global asymptotic properties the equivariant projector associated to a
weight $k \, \boldsymbol{ \nu }$, when $\boldsymbol{ \nu }$ is fixed and
$k\rightarrow +\infty$.
