Good Representations and Homogeneous Spaces

Abstract

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to study representations of G, representations of H which are induced from representations of G, and intersections of reductive subgroups of G.

v2: Added caveat at the beginning in regards to these results already existing in the literature. 8 pages