Hamiltonian Carleman approximation and the density property for coadjoint orbits

For a complex Lie group $G$ with a real form $G_0 \subset G$, we prove that any Hamiltonian automorphism $\phi$ of a coadjoint orbit $\mathcal{O}_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic $\mathcal{O}_0$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $\mathcal{O}$ is closed. In the course of the proof, we establish the Hamiltonian density property for closed coadjoint orbits of all complex Lie groups.

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Received 20 February 2021

Accepted 26 April 2021

Published 16 May 2022