Symplectic leaves of W-algebras from the reduced Kac-Moody point of view
Abstract
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 (W2) (Virasoro) algebra is investigated in detail, where the positivity of the energy functional is also analyzed.
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