数学学科2025系列学术报告之十三

　　报告题目：Representation and tensor category of affine sl_2 at positive rational levels

　　报告人：杨进伟教授（上海交通大学）

　　时 间：2025年6月19日 10:00-11:00

　　地点：理学院1号楼1-301

　　摘要：In a series of celebrated work, Kazhdan and Lusztig constructed braided tensor category structure on the category of finite length modules for the affine Lie algebras when the level plus dual Coxeter number is not a postive rational number, and proved that the category is equivalent to the category of quantum groups at the corresponding parameter. In this talk, we discuss our recent progress on tensor categories at postive rational levels using vertex operator algebra approach. Concretely, We construct braided tensor category structure on the category of ordinary modules for simple affine vertex operator algebras and prove rigidity in some cases. For affine sl_2 Lie algebra, we also study the category of finite length generalized modules for the universal affine vertex operator algebra, we show this category is derived equivalent to the category of the quantum groups at the corresponding parameter.

　　报告人简介：杨进伟，上海交通大学副教授，本科和硕士毕业于北京大学数学学院，师从张继平院士，2014年在罗格斯大学取得博士学位，导师为黄一知教授。他的主要研究领域为李理论，表示论和张量范畴理论，尤其是用顶点算子代数的张量范畴理论来研究李代数、量子群、顶点算子代数等代数对象的表示和张量范畴结构及其对应关系。主要研究成果发表在Math. Ann., Adv. Math., Comm. Math. Phys., IMRN等期刊上。