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Towards a symplectic version of the Chevalley restriction theorem

  • Michael Bulois (a1), Christian Lehn (a2), Manfred Lehn (a3) and Ronan Terpereau (a4) (a5)

Abstract

If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak{c}$ and Weyl group $W$ , it is shown that there is a natural morphism of Poisson schemes $\mathfrak{c}\oplus \mathfrak{c}^{\ast }/W\rightarrow V\oplus V^{\ast }/\!\!/\!\!/G$ . This morphism is conjectured to be an isomorphism of the underlying reduced varieties if $(G,V)$ is visible. The conjecture is proved for visible stable locally free polar representations and some other examples.

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