Abstract: We discuss the branching problem for generalized Verma modules applied to couples of reductive Lie algebras. The analysis is based on projecting character formulas to quantify the branching, and on projections using the center of U(\bar{\mathfrak g}) to explicitly construct singular vectors realizing (part of) the branching. We demonstrate the results on the pair (SO(7),G₂) for both compatible and non-compatible parabolic subalgebras and a large class of inducing representations.