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

TL;DR

This paper investigates the geometric and algebraic properties of spherical nilpotent orbit closures in the isotropy representations of classical non-Hermitian symmetric pairs, focusing on normality and module structures.

Contribution

It provides a detailed analysis of the normality and K-module structure of orbit closures in classical non-Hermitian symmetric pairs, a topic not extensively explored before.

Findings

Determined normality of all such orbit closures.

Described the K-module structure of their rings of regular functions.

Provided explicit descriptions for the 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.