Symplectic leaves of W-algebras from the reduced Kac-Moody point of view

The symplectic leaves of W-algebras are the intersections of the symplectic leaves of the Kac-Moody algebras and the hypersurface of the second class constraints, which define the W-algebra. This viewpoint enables us to classify the symplectic leaves and also to give a representative for each of them. The case of the (W_{2}) (Virasoro) algebra is investigated in detail, where the positivity of the energy functional is also analyzed.