Towards a symplectic version of the Chevalley restriction theorem

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 $\mathfrak{c}\oplus {\mathfrak{c}}^{\ast }/W\to V\oplus V^{\ast }///G$. 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 certain further examples.

18 pages, final version

References in corpus (2)

• Schémas de Hilbert invariants et théorie classique des invariants
• Invariants of commuting matrices

Cited by in corpus (3)

• Symplectic quotients have symplectic singularities
• All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces
• Invariant holonomic systems on symmetric spaces and other polar representations