Regular functions on spherical nilpotent orbits in complex symmetric pairs: Classical non-Hermitian cases

Abstract

Given a classical semisimple complex algebraic group $G$ and a symmetric pair $(G,K)$ of non-Hermitian type, we study the closures of the spherical nilpotent $K$-orbits in the isotropy representation of $K$. For all such orbit closures, we study the normality, and we describe the $K$-module structure of the ring of regular functions of the normalizations.