Degeneration of groups of type E7 and minimal coupling in supergravity

We study properties of D = 4 N >= 2 extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity. This involves a detailed classification of the "degenerations" of the duality groups of type E-7, when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G(4) "degenerates" into a perfect square. With regard to cosmological applications, minimal coupling of vectors in consistent truncation to N = 1 from higher-dimensional or higher-N theory is non-generic. On the other hand, non-minimal coupling involving vectors coupled to scalars and axions is generic. These features of supergravity, following from the electric-magnetic duality, may be useful in other applications, like stabilization of moduli, and in studies of non-perturbative black-hole solutions of supergravity/string theory.