Towards a symplectic version of the Chevalley restriction theorem

Abstract : If $(G, V)$ is a polar representation with Cartan subspace $c$ 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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Contributor : Michael Bulois <>
Submitted on : Wednesday, March 29, 2017 - 10:44:27 PM
Last modification on : Friday, May 10, 2019 - 10:59:36 AM
Long-term archiving on : Friday, June 30, 2017 - 5:13:44 PM

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Michael Bulois, Christian Lehn, Manfred Lehn, Ronan Terpereau. Towards a symplectic version of the Chevalley restriction theorem. Compositio Mathematica, Foundation Compositio Mathematica, 2017, 153 (3), pp.647-666. ⟨10.1112/S0010437X16008277⟩. ⟨hal-01308641⟩

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