Embeddings of homogeneous spaces into irreducible modules

Abstract

Let $G$ be a connected reductive group. We find a necessary and sufficient condition for a quasiaffine homogeneous space of $G$ to be embeddable into an irreducible $G$-module. In addition, for an affine homogeneous space we find a criterium for a closed embedding to exist

v2 8 pages, a gap in the proof is corrected, some examples are added v3 new theorem answering whether there is a closed embedding is added