Some Problems in Representation Theory and Algebraic Geometry

本课题是研究量子群的局域化构造，重点研究统一情况下的根。它是Alex Rosenberg联合项目的延续，在这个项目中，本地化是为通用情况构建的。该项目的第二部分是研究在代数变体变形中出现的Kodaira-Spencer李代数。这是最近与爱德华·路易延加（edward Looijenga）合作开发的“镜像双重”图片。量子群是最近在物理学中出现的代数对象。然而，这些对象的研究不仅可以应用于物理学，也可以用于研究纯代数性质的各种问题。

LUNTS 97-00964 This project is a study of the localization construction for quantum groups with emphasis on the roots of unity case. It is a continuation of the joint project with Alex Rosenberg where the localization was constructed for the generic case. The second part of the project is the study of the Kodaira-Spencer Lie algebra which arises in deformations of algebraic varieties. This is the "mirror dual" picture to the one developed recently with Eduard Looijenga. Quantum groups are algebraic objects which have recently arisen from physics. However, these objects whose study not only has applications to physics can also be used to study various questions of a purely algebraic nature.