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

Abstract

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

v2, 39 pages, 11 tables, section 3.2 rewritten in more explicit terms. This is the second in a series of papers initiated by arXiv:1602.07141. Final version, to appear in Kyoto Journal of Mathematics

References in corpus (4)

• Normalizers of solvable spherical subgroups
• Projective normality of model varieties and related results
• Regular functions on spherical nilpotent orbits in complex symmetric pairs: classical non-Hermitian cases
• Standard monomial theory for wonderful varieties