论文标题
半无限环境中的同源方法
Homological methods in semi-infinite contexts
论文作者
论文摘要
代数组在DG类别上的作用在几何表示理论的某些部分，尤其是还原性谎言代数的代表理论中提供了方便，统一的框架。我们将这一理论扩展到循环群体和主张代数，从而扩展了Beraldo，Gaitsgory和作者的先前工作。 在此过程中，我们介绍了一些独立感兴趣的主题：无限类型的Indschemes，拓扑DG代数以及类别群在类别上的较弱的作用。我们还基于循环基团的模块化特征，为仿射代数的半无限同种学的新结构提供了新的结构。 作为我们方法的应用，我们在临界级别建立了KAC-MOODY代表的重要技术结果，表明表征的适当（“重新归一化”）派生的类别承认，来自Loop组的伴随行动以及来自封闭代数的中心。
Actions of algebraic groups on DG categories provide a convenient, unifying framework in some parts of geometric representation theory, especially the representation theory of reductive Lie algebras. We extend this theory to loop groups and affine Lie algebras, extending previous work of Beraldo, Gaitsgory and the author. Along the way, we introduce some subjects of independent interest: ind-coherent sheaves of infinite type indschemes, topological DG algebras, and weak actions of group indschemes on categories. We also present a new construction of semi-infinite cohomology for affine Lie algebras, based on a modular character for loop groups. As an application of our methods, we establish an important technical result for Kac-Moody representations at the critical level, showing that the appropriate ("renormalized") derived category of representations admits a large class of symmetries coming from the adjoint action of the loop group and from the center of the enveloping algebra.
