Embeddings of homogeneous spaces into irreducible modules

Abstract

Let G be a connected reductive algebraic group. We find a necessary and sufficient condition for a quasi-affine homogeneous space [G over H] to have an embedding into an irreducible G-module. For reductive H we also find a necessary and sufficient condition for a closed embedding of [G over H] into an irreducible module to exist. These conditions are stated in terms of the group of central automorphisms of [G over H].