论文标题
谎言代数行动在模块类别上的截断扬吉亚人的模块类别
Lie algebra actions on module categories for truncated shifted Yangians
论文作者
论文摘要
从Braverman-Finkelberg-Nakajima的意义上讲，我们开发了一种抛物线诱导和限制函数，该理论将模块与库仑分支代数相关。我们的函子将bezrukavnikov-etingof的归纳和限制性函数概括为Cherednik代数，但它们的定义使用了不同的工具。 在经过这个一般定义之后，我们重点介绍箭量$γ$的箭量规定。诱导和限制函数使我们能够定义相应的对称的Kac-Moody代数$ \ Mathfrak {G}_γ$的分类动作，用于这些库仑分支代数。当$γ$是Dynkin类型的$γ$时，库仑分支代数将被截断为延而扬吉亚人，并量化了广义的仿生草片。因此，我们将行动视为几何萨克对应关系的分类。 为了建立这种分类动作，我们定义了一类新的“调味” KLRW代数，该代数类似于第二作者最初为张量产品分类而制造的图解代数。我们证明了库仑分支代数上的gelfand-tsetlin模块类别与调味的KLRW代数上的模块之间的等效性。这种等效性通过归纳和限制函子与KLRW代数对模块的常规分类作用进行分类作用。
We develop a theory of parabolic induction and restriction functors relating modules over Coulomb branch algebras, in the sense of Braverman-Finkelberg-Nakajima. Our functors generalize Bezrukavnikov-Etingof's induction and restriction functors for Cherednik algebras, but their definition uses different tools. After this general definition, we focus on quiver gauge theories attached to a quiver $Γ$. The induction and restriction functors allow us to define a categorical action of the corresponding symmetric Kac-Moody algebra $\mathfrak{g}_Γ$ on category $ \mathcal O $ for these Coulomb branch algebras. When $ Γ$ is of Dynkin type, the Coulomb branch algebras are truncated shifted Yangians and quantize generalized affine Grassmannian slices. Thus, we regard our action as a categorification of the geometric Satake correspondence. To establish this categorical action, we define a new class of "flavoured" KLRW algebras, which are similar to the diagrammatic algebras originally constructed by the second author for the purpose of tensor product categorification. We prove an equivalence between the category of Gelfand-Tsetlin modules over a Coulomb branch algebra and the modules over a flavoured KLRW algebra. This equivalence relates the categorical action by induction and restriction functors to the usual categorical action on modules over a KLRW algebra.
