Multiplicity in root components via geometric Satake

In this note we explicitly construct top-dimensional components of certain cyclic convolution varieties. These correspond (via the geometric Satake equivalence) to irreducible summands V(λ+μ−Nβ)⊂V(λ)⊗V(μ) for SLn+1(C), where N≥1 and β is a positive root. Furthermore, deduce from these constructions nontrivial lower bound on multiplicity subrepresentations when not simple Finally, demonstrate that all such can be realized as closures orbits.