Irreducible unitary representations of the group \(\text{Diff}(S^ 2,\omega)\) of functional dimension two (Q1178117)

The author defines the representations of the Lie algebra \(C^ \infty(S^ 2)\) in the space of all functions on \(E=S^ 3\); it is given the decomposition of these representations in irreducible representations and it is proved the integrability on the group \(\text{Diff}(S^ 2,\omega)\) of symplectic diffeomorphisms of two-dimensional sphere. Finally, the author gives the extension of the obtained construction to study the structure of irreducible unitary representations for the group \(\text{Diff}(M^{2n},\omega)\) of symplectic diffeomorphisms of an arbitrary compact symplectic manifold, provided that the 2-form \(\omega\) satisfies the integrability condition.