  A space of polynomials V of dimension 7 is called self-dual if the divided
Wronskian of any 6-subspace is in V. A self-dual space V has a natural inner
product. The divided Wronskian of any isotropic 3-subspace of V is a square of
a polynomial. We call V self-self-dual if the square root of the divided
Wronskian of any isotropic 3-subspace is again in V. We show that the
self-self-dual spaces have a natural non-degenerate skew-symmetric 3-form
defined in terms of Wronskians.
  We show that the self-self-dual spaces correspond to G_2-populations related
to the Bethe Ansatz of the Gaudin model of type G_2 and prove that a
G_2-population is isomorphic to the G_2 flag variety.
