Multiplicity in root components via geometric Satake. Issue 6 (3rd June 2022) - Besson, Marc; Jeralds, Sam; Kiers, Joshua
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 V ( λ + μ − N β ) ⊂ V ( λ ) ⊗ V ( μ ) for S L n + 1 ( C ), where N ≥ 1 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.