Representation Theory and Conformal Field Theory

Malikov 97-01589该方案的三个主题是：仿射李代数上的Harish-Chandra双模，向量丛的模的可容许表示的局部化和圆的同胚群的李代数。将使用的主要工具是g-模的Bernstein-Beilinson局部化技术和起源于现代物理学的相关思想，例如Kazhdan-Lusztig张量和顶点算子代数在过去十年中见证了来自量子物理和数学的思想的壮观相互作用。这项提议是关于这些思想的融合。这些结果可能在共形场理论、表示理论、几何和低维拓扑中得到应用。

ABSTRACT Malikov 97-01589 The three topics of the proposal are: Harish-Chandra bimodules over affine Lie algebras, localization of admissible representations to the moduli of vector bundles and a Lie algebra of the group of homeomorphisms of the circle. The main tools to be employed are the Bernstein-Beilinson technique of localization of g-modules and related ideas originating in modern physics, for example Kazhdan-Lusztig tensoring and vertex operator algebras The last decade has seen a spectacular interplay of ideas coming from quantum physics and mathematics. This proposal is about the fusion of these ideas. The results might find application in conformal field theory, representation theory, geometry and low dimensional topology.