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

摘要

Given a classical semisimple complex algebraic group G and a symmetric pair (G,K) of Hermitian type, we study the closures of the spherical nilpotentK-orbits in the isotropy representation ofK.We show that all such orbit closures are normal and describe the K-module structure of their ring of regular functions.