  In this work we extend the Mackey's theory of induced unitary representations
on a wide class of Krein-isometric induced representations in Krein spaces. The
subgroup theorem and the Kronecker product theorem are shown to be valid for
the induced representations of this class. Among the class of representations
which are subsumed by this extension there are all the representations acting
in the single particle Krein-Hilbert space and in Fock-Krein spaces of the mass
less gauge free fields underling the Standard Model in the local gauge BRST
formalutaion, e. g. of the electromagnetic potential field.
