Abstract
In this thesis, we obtain the branching laws from so(7, C) to g₂ of the generalized Verma modules attached to the g₂-compatible parabolic subalgebras of so(7, C), and the branching laws from g₂ to sl(3, C) of the generalized Verma modules attached to the sl(3, C)-compatible parabolic subalgebras of g₂ respectively, under some assumptions on the parameters of the generalized Verma modules. Then, we apply the branching formulas to homogeneous spaces by showing a generalization of correspondence theorem. Finally, we return to discuss and classify the compatible parabolic subalgebras for complex symmetric pairs.