A classification of irreducible weakly spherical homogeneous spaces

In this paper, we classify all homogeneous spaces ρ(H)\GL(V) with an open dense P-orbit, except when (GL1×H,Λ1⊗ρ,V(1)⊗V) is a trivial P.V., where P is a proper parabolic subgroup of GL(V) and ρ:H→GL(V) is a finite-dimensional irreducible representation of a semisimple algebraic group H. When P is of type P(e1,e2,e3), we classify all the cases up to equivalence. We consider everything over the complex number field C.