  We show there is a class of symplectic Lie algebra representations over any
field of characteristic not 2 or 3 that have many of the exceptional algebraic
and geometric properties of both symmetric three forms in two dimensions and
alternating three forms in six dimensions. All nonzero orbits are coisotropic
and the covariants satisfy relations generalising classical identities of
Eisenstein and Mathews. The main algebraic result is that suitably generic
elements of these representation spaces can be uniquely written as the sum of
two elements of a naturally defined Lagrangian subvariety. We give universal
explicit formulae for the summands and show how they lead to the existence of
geometric structure on appropriate subsets of the representation space. Over
the reals this structure reduces to either a conic, special pseudo-K\" ahler
metric or a conic, special para-K\" ahler metric.
