Multiplicity in root components via geometric Satake
Abstract In this note we explicitly construct top-dimensional components of certain cyclic convolution varieties. These components correspond (via the geometric Satake equivalence) to irreducible summands for where and β is a positive root. Furthermore, we deduce from these constructions a nontrivial lower bound on the multiplicity of these subrepresentations when β is not a simple root. Finally, we demonstrate that not all such top-dimensional components can be realized as closures of orbits.