Regular functions on spherical nilpotent orbits in complex symmetric pairs: exceptional 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 G2, and compute the K-module structure of the ring of regular functions on their normalizations.

39 pages, 12 tables. This is the last in a series of papers initiated by arXiv:1602.07141 and arXiv:1612.01300