Towards a symplectic version of the Chevalley restriction theorem
Bulois, Michael ; Lehn, Christian ; Lehn, Manfred ; Terpereau, Ronan
HAL, hal-01308641 / Harvested from HAL
Text on HAL
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.
Publié le : 2017-03-04
Classification:  Reductive group,  Symplectic variety,  Symplectic reduction,  Moment map,  Polar representation,  MSC: 14L30, 53D20, 20G05, 20G20, 13A50,  [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] 
@article{hal-01308641,
     author = {Bulois, Michael and Lehn, Christian and Lehn, Manfred and Terpereau, Ronan},
     title = {Towards a symplectic version of the Chevalley restriction theorem},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01308641}
}

Bulois, Michael; Lehn, Christian; Lehn, Manfred; Terpereau, Ronan. Towards a symplectic version of the Chevalley restriction theorem. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01308641/