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If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak c$ andWeyl group $W$, it is shown that there is a natural morphism of Poisson schemes$\mathfrak c \oplus {\mathfrak c}^*/W \to V\oplus V^*/\!\!/\!\!/ G$. Thismorphism is conjectured to be an isomorphism of the underlying reducedvarieties if $(G,V)$ is visible. The conjecture is proved for visible stablelocally free polar representations and certain further examples.

Towards a symplectic version of the Chevalley restriction theorem