Let X be a Poisson variety with a Hamiltonian G-action and H be a normal subgroup of G. Then X//G is obtained by a (Hamiltonian) reduction of X//H by the induced G/H-action under suitable assumptions, called reduction by stages. We apply for the Slodowy slices and show that the Slodowy slice associated to (π€,πͺ) is obtained by a reduction of the Slodowy slice associated to (π€,πͺβ) for a simple Lie algebra π€ and nilpotent orbits πͺ, πͺβ such that πͺ > πͺβ with some conditions. The quantum cases imply that the finite/affine W-algebras associated to (π€,πͺ) are obtained by W-algebras associated to (π€,πͺβ), which proves a conjecture of Morgan in finite cases and gives a conjectural generalization of results of Madsen and Ragoucy in affine cases.
This is a joint work with Thibault Juillard.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Geometric Representation Theory and W-algebras.
