Ind_H^G V = G-rep induced from H-rep V via tensor product k[G] ⊗_{k[H]} V. Frobenius-reciprocity Hom_G(Ind W, V) = Hom_H(W, Res V). Mackey theory generalises.
Ind_H^G V = G-rep induced from H-rep V via tensor product k[G] ⊗_{k[H]} V. Frobenius-reciprocity Hom_G(Ind W, V) = Hom_H(W, Res V). Mackey theory generalises.