Basic differential forms for actions of Lie groups

Source abstract

A section of a Riemannian G G -manifold M M is a closed submanifold Σ \Sigma which meets each orbit orthogonally. It is shown that the algebra of G G -invariant differential forms on M M which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on Σ \Sigma which are invariant with respect to the generalized Weyl group of Σ \Sigma , under some condition.