On the Homotopy of Symplectomorphism Groups of Homogeneous Spaces

Abstract

Let $\mathcal{O}$ be a quantizable coadjoint orbit of a semisimple Lie group $G$. Under certain hypotheses we prove that $#(π_1(\text{Ham}({\cal O})))\geq #(Z(G))$, where $\text{Ham}(\mathcal{O})$ is the group of Hamiltonian symplectomorphisms of $\mathcal{O}$.

6 pages. Added new reference. Proposition 4 corrected

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