  Starting from the symplectic construction of the Lie algebra e_7(7) due to
Adams, we consider an Iwasawa parametrization of the coset E_7(7)/SU(8), which
is the scalar manifold of N=8, d=4 supergravity. Our approach, and the manifest
off-shell symmetry of the resulting symplectic frame, is determined by a
non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E_7(7). In
absence of gauging, we utilize the explicit expression of the Lie algebra to
study the origin of E_7(7)/SU(8) as scalar configuration of a 1/8-BPS extremal
black hole attractor. In such a framework, we highlight the action of a U(1)
symmetry spanning the dyonic 1/8-BPS attractors. Within a suitable
supersymmetry truncation allowing for the embedding of the Reissner-Nordstrom
black hole, this U(1) is interpreted as nothing but the global R-symmetry of
pure N=2 supergravity. Moreover, we find that the above mentioned U(1) symmetry
is broken down to a discrete subgroup Z_4, implying that all 1/8-BPS Iwasawa
attractors are non-dyonic near the origin of the scalar manifold. We can trace
this phenomenon back to the fact that the Cartan subalgebra of SL(8,R) used in
our construction endows the symplectic frame with a manifest off-shell
covariance which is smaller than SL(8,R) itself. Thus, the consistence of the
Adams-Iwasawa symplectic basis with the action of the U(1) symmetry gives rise
to the observed Z_4 residual non-dyonic symmetry.
