论文标题
通过有限的W-Algebras进行减少
Reduction by stages for finite W-algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为简单的谎言代数：其双空间$ \ mathfrak {g}^*$是泊松品种。众所周知，对于$ \ mathfrak {g} $中的每个nilpotent元素$ f $，可以通过汉密尔顿还原构建一种新的泊松结构，这与$ \ mathfrak {g}^*$的某种亚变量是同构的，Slodowy slice slice slice $ s_f $。给定两个nilpotent元素$ f_1 $和$ f_2 $带有某些兼容性假设，我们通过阶段证明汉密尔顿的减少：slice $ s_ {f_2} $是汉密尔顿的减少slice $ s_ $ s_s_ {f_1} $。我们还在有限的W-偏骨架的设置中陈述了类似的结果，该量子是slos的slices片的量化。这些结果是由摩根在他的博士学位论文中猜想的。作为A型推论，我们证明可以从任何其他挂钩型中获得任何挂钩型W-Algebra。作为应用程序，我们建立了史学他的等效性的概括。最后，我们在仿射W-Algebras的背景下做出了一些猜想。
Let $\mathfrak{g}$ be a simple Lie algebra: its dual space $\mathfrak{g}^*$ is a Poisson variety. It is well known that for each nilpotent element $f$ in $\mathfrak{g}$, it is possible to construct a new Poisson structure by Hamiltonian reduction which is isomorphic to some subvariety of $\mathfrak{g}^*$, the Slodowy slice $S_f$. Given two nilpotent elements $f_1$ and $f_2$ with some compatibility assumptions, we prove Hamiltonian reduction by stages: the slice $S_{f_2}$ is the Hamiltonian reduction of the slice $S_{f_1}$. We also state an analogous result in the setting of finite W-algebras, which are quantizations of Slodowy slices. These results were conjectured by Morgan in his PhD thesis. As corollary in type A, we prove that any hook-type W-algebra can be obtained as Hamiltonian reduction from any other hook-type one. As an application, we establish a generalization of the Skryabin equivalence. Finally, we make some conjectures in the context of affine W-algebras.
