Regular functions on spherical nilpotent orbits in complex symmetric pairs: Classical Hermitian 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 G 2 , and compute the K-module structure of the ring of regular functions on their normalizations.