Abstract
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.