Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2003.09356 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $\mathfrak{g}$ be a simple classical Lie algebra over $\mathbb{C}$ and $G$ be the adjoint group. Consider a nilpotent element $e\in \mathfrak{g}$, and the adjoint orbit $\mathbb{O}=Ge$. The formal slices to the codimension $2$ orbits in the closure $\overline{\mathbb{O}}\subset \mathfrak{g}$ are well-known due to the work of Kraft and Procesi. In this paper, we prove a similar result for the universal $G$-equivariant cover $\widetilde{\mathbb{O}}$ of $\mathbb{O}$. Namely, we describe the codimension $2$ singularities for its affinization $Spec(\mathbb{C}[\widetilde{\mathbb{O}}])$.