论文标题
通用过滤的nilpotent Slodowy Slices的量化
Universal filtered quantizations of nilpotent Slodowy slices
论文作者
论文摘要
由于Losev和Namikawa的工作，每个圆锥形的象征性奇异性都承认了普遍的泊松变形和通用过滤的量化。我们通过表明每个这样的品种都接受了通用的泊松变形和通用的量化量化，从而开始了本文。 我们继续研究这些定义在尼尔氏静态slos缝的背景下。首先，我们对有限的$ W $ -Algebra是对切片的普遍过滤量化的案例进行完整的描述，这是基于Lehn-namikawa-Sorger的工作。这导致了对Nilpotent Slodowy Slices的过滤量化的几乎完整的分类。 非固定的谎言代数中的次规则切片特别有趣：由于对Dynkin类型的一些较小限制，我们证明有限的$ W $ -Algebra是关于Dynkin Kutomormormings的普遍性量化量，从Dynkin Daugram的展开中产生。这可以看作是Slodowy定理的非共同类似物。最后，我们将此结果应用于B型中的次规则有限$ W $ - 代数作为转移的Yangian的商。
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every such variety admits a universal equivariant Poisson deformation and a universal equivariant quantization with respect to a reductive group acting on it by $\mathbb{C}^\times$-equivariant Poisson automorphisms. We go on to study these definitions in the context of nilpotent Slodowy slices. First we give a complete description of the cases in which the finite $W$-algebra is a universal filtered quantization of the slice, building on the work of Lehn--Namikawa--Sorger. This leads to a near-complete classification of the filtered quantizations of nilpotent Slodowy slices. The subregular slices in non-simply-laced Lie algebras are especially interesting: with some minor restrictions on Dynkin type we prove that the finite $W$-algebra is a universal equivariant quantization with respect to the Dynkin automorphisms coming from the unfolding of the Dynkin diagram. This can be seen as a non-commutative analogue of Slodowy's theorem. Finally we apply this result to give a presentation of the subregular finite $W$-algebra in type B as a quotient of a shifted Yangian.
