A classification of irreducible weakly spherical homogeneous spaces (Q855743)

The authors classify all homogeneous spaces \(\rho(H)|\text{GL}(V)\) with an open dense \(P\)-orbit, except when \(\text{GL}_1\times H,\,\Lambda_1\otimes\rho,\, V(1)\otimes V)\) is a trivial prehomogeneous vector space, where \(P\) is a proper parabolic subgroup of \(\text{GL}(V)\) and \(\rho: H\to \text{GL}(V)\) is a finite-dimensional irreducible representation of a semisimple algebraic group \(H\). When \(P\) is of type \(P(e_1,e_2,e_3)\), they classify all the cases up to equivalence. The classification is done over the complex number field.