Polynomially convex orbits of compact lie groups

Abstract

LetV be a finite dimensional complex linear space and letG be a compact subgroup of GL(V). We prove that an orbitGυ, υ ∈ V, is polynomially convex if and only ifGℂυ is closed andGυ is the real form ofGℂυ. For every orbitGυ which is not polynomially convex we construct an analytic annulus or strip inGℂυ with the boundary inGυ. It is also proved that the group of holomorphic automorphisms ofGℂυ which commute withGℂ acts transitively on the set of polynomially convexG-orbits. Further, an analog of the Kempf-Ness criterion is obtained and homogeneous spaces of compact Lie groups which admit only polynomially convex equivariant embeddings are characterized.