  In M-theory vacua with vanishing 4-form F, one can invoke the ordinary
Riemannian holonomy H \subset SO(1,10) to account for unbroken supersymmetries
n=1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid
for non-zero F, can account for more exotic fractions of supersymmetry, in
particular 16<n<32. The conjectured holonomies are given by H \subset G where G
are the generalized structure groups G=SO(d-1,1) x G(spacelike), G=ISO(d-1) x
G(null) and G=SO(d) x G(timelike) with 1<=d<11. For example,
G(spacelike)=SO(16), G(null)=[SU(8) x U(1)] \ltimes R^{56} and
G(timelike)=SO*(16) when d=3. Although extending spacetime symmetries, there is
no conflict with the Coleman-Mandula theorem. The holonomy conjecture rules out
certain vacua which are otherwise permitted by the supersymmetry algebra.
