  We give applications of Foliation Theory to the Classical Invariant Theory of
real orthogonal representations, including: The solution of the Inverse
Invariant Theory problem for finite groups. An if-and-only-if criterion for
when a separating set is a generating set. And the introduction of a class of
generalized polarizations which, in the case of representations of finite
groups, always generates the algebra of invariants of their diagonal
representations.
