论文标题
Aggine $ W $ -Elgebras的本地化
Localization for affine $W$-algebras
论文作者
论文摘要
我们证明了本地化定理$ w $ - 代数，本着贝林森 - 伯恩斯坦和喀什瓦拉 - 塔尼萨基的精神。更确切地说，对于任何非关键的常规重量$λ$，我们都会在增强的仿射标志品种上确定$λ$ -Minodromic Whittaker $ d $ modules，其中包含$ w $ w $ -algebra的类别$ \ mathscr {o} $的完整子类别。为了识别函数的基本图像，我们使用iWahori-whittaker模块为相应的kac-moody代数提供了类别$ \ mathscr {o} $的新实现。使用这些方法，我们还获得了Arakawa的角色公式的新证明，用于简单的$ W $ -Algebra。
We prove a localization theorem for affine $W$-algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight $λ$, we identify $λ$-monodromic Whittaker $D$-modules on the enhanced affine flag variety with a full subcategory of Category $\mathscr{O}$ for the $W$-algebra. To identify the essential image of our functor, we provide a new realization of Category $\mathscr{O}$ for affine $W$-algebras using Iwahori--Whittaker modules for the corresponding Kac--Moody algebra. Using these methods, we also obtain a new proof of Arakawa's character formulae for simple positive energy representations of the $W$-algebra.
