Regular functions on spherical nilpotent orbits in complex symmetric pairs: Exceptional cases

Abstract

Given an exceptional simple complex algebraic group $G$ and a symmetric pair $(G,K)$, we study the spherical nilpotent $K$-orbit closures in the isotropy representation of $K$. We show that they are all normal except in one case in type ${\mathsf{G}}_2$, and we compute the $K$-module structure of the ring of regular functions on their normalizations.