Slodowy Slices and Universal Poisson Deformations

TL;DR

This paper classifies certain nilpotent orbits in simple Lie algebras where the Slodowy slice's restriction yields universal Poisson deformations, revealing new singular symplectic hypersurfaces of dimensions 4 and 6.

Contribution

It generalizes previous work by identifying new cases where Slodowy slices produce universal Poisson deformations, expanding understanding of singular symplectic hypersurfaces.

Findings

Classification of nilpotent orbits with universal Poisson deformations

Discovery of new singular symplectic hypersurfaces of dimensions 4 and 6

Extension of Brieskorn and Slodowy's work on subregular orbits

Abstract

We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension 4 and 6.