Denote the equivalence class of (g,x) by [g,x]. Note that this equivalence relation is invariant under the action of ; consequently, acts on . The latter is a vector bundle over the quotient space with as the structure group and as the fiber. Let be the space of sections \phi : G/H \to (G \times V)/ \! \sim of this vector bundle. This is the vector space underlying the induced representation . The group acts on a section \phi : G/H \to \mathcal L_W given by gH \mapsto [g,\phi_g] as follows:
