On the affinization of a nilpotent orbit cover

Abstract

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 $\tilde{\mathbb{O}}$ of $\mathbb{O}$. Namely, we describe the codimension $2$ singularities for its affinization $Spec(\mathbb{C}[\tilde{\mathbb{O}}])$.

I am grateful to Shilin Yu for pointing out a mistake in the first version of the paper. The second version includes description of symmetries acting on the codimension 2 singularities, and a discussion of expected symplectic duality, which this paper provides evidence to

References in corpus (2)

• Induced nilpotent orbits and birational geometry
• Birational geometry for the covering of a nilpotent orbit closure

Cited by in corpus (1)

• Birational geometry for the covering of a nilpotent orbit closure