Arkiv för Matematik

Volume 60 (2022)

Number 1

Hamiltonian Carleman approximation and the density property for coadjoint orbits

Pages: 23 – 41



Fusheng Deng (School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China)

Erlend Fornæss Wold (Matematisk Institutt, Universitetet i Oslo, Norway)


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.

Received 20 February 2021

Accepted 26 April 2021

Published 16 May 2022