论文标题
关于nilpotent轨道覆盖的影响
On the affinization of a nilpotent orbit cover
论文作者
论文摘要
令$ \ mathfrak {g} $为$ \ mathbb {c} $，而$ g $为伴随组的简单古典谎言代数。考虑一个nilpotent元素$ e \ in \ mathfrak {g} $，以及伴随轨道$ \ mathbb {o} = ge $。封闭式$ \ overline {\ mathbb {o}}} \ subset \ mathfrak {g} $中的codimension $ 2 $ orbits的正式切片是由于Kraft和Procesi的工作而众所周知的。在本文中，我们证明了$ \ mathbb {o} $的通用$ g $ equivariant cover $ \ wideTilde {\ mathbb {o}} $。也就是说，我们描述了$ 2 $ 2 $ singularities $ spec（\ mathbb {c} [\ widetilde {\ mathbb {o}}}]）$。
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 $Spec(\mathbb{C}[\widetilde{\mathbb{O}}])$.
