Towards a symplectic version of the Chevalley restriction theorem
Résumé
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.
| Origine | Fichiers produits par l'(les) auteur(s) |
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