  We discuss the degeneracies of 4D and 5D BPS black holes in toroidal
compactifications of M-theory or type II string theory, using U-duality as a
tool. We generalize the 4D/5D lift to include all charges in N=8 supergravity,
and compute the exact indexed degeneracies of certain 4D 1/8-BPS black holes.
Using the attractor formalism, we obtain the leading micro-canonical entropy
for arbitrary Legendre invariant prepotentials and non-vanishing D6-brane
charge. In particular, we find that the N=8 prepotential is given to leading
order by the cubic invariant of $E_6$. This suggests that the minimal unitary
representation of $E_8$, based on the same cubic prepotential, underlies the
microscopic degeneracies of N=8 black holes. We propose that the exact
degeneracies are given by the Wigner function of the $E_8(Z)$ invariant vector
in this automorphic representation. A similar conjecture relates the
degeneracies of N=4 black holes to the minimal unipotent representation of
$SO(8,24,Z)$.
