  To any Hamiltonian action of a reductive algebraic group $G$ on a smooth
irreducible symplectic variety $X$ we associate certain combinatorial
invariants: Cartan space, Weyl group, weight and root lattices. For cotangent
bundles our invariants essentially coincide with those arising in the theory of
equivarant embeddings. Using our approach we establish some properties of the
latter invariants.

Algebraic Geometry;Representation Theory;Symplectic Geometry