  In this note we explicitly construct top-dimensional components of the cyclic
convolution varieties. These components correspond (via the geometric Satake
equivalence) to irreducible summands $V(\lambda+\mu-N\beta) \subset V(\lambda)
\otimes V(\mu)$ for $G^\vee=SL_{n+1}$, where $N\ge 1$ and $\beta$ is a positive
root. Furthermore, we deduce from these constructions a nontrivial lower bound
on the multiplicity of these subrepresentations when $\beta$ is not a simple
root. Finally, we demonstrate that not all such top-dimensional components can
be realized as closures of orbits.
