Deformations of nilpotent cones and Springer correspondences

TL;DR

This paper introduces a deformation of the nilpotent cone for the symplectic group Sp(2n), linking classical and exotic Springer correspondences across different characteristics, and provides a complete description of the exotic correspondence.

Contribution

It presents a new deformation of the nilpotent cone for Sp(2n) that connects classical and exotic Springer correspondences, offering a comprehensive understanding of the exotic case.

Findings

Established a deformation linking Springer correspondences in different characteristics

Provided a complete description of the exotic Springer correspondence

Connected classical and exotic Springer theories through this deformation

Abstract

Let G = Sp (2n) be the symplectic group over Z. We present a certain kind of deformation of the nilpotent cone of G with G-action. This enables us to make direct links between the Springer correspondence of sp_{2n} over C, that over characteristic two, and our exotic Springer correspondence. As a by-product, we obtain a complete description of our exotic Springer correspondence.