報告題目：Representation and tensor category of affine sl_2 at positive rational levels

　　報告人：楊進偉教授（上海交通大學）

　　時 間：2025年6月19日 10:00-11:00

　　地點：理學院1號樓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.

　　報告人簡介：楊進偉，上海交通大學副教授，本科和碩士畢業于北京大學數學學院，師從張繼平院士，2014年在羅格斯大學取得博士學位，導師為黃一知教授。他的主要研究領域為李理論，表示論和張量范疇理論，尤其是用頂點算子代數的張量范疇理論來研究李代數、量子群、頂點算子代數等代數對象的表示和張量范疇結構及其對應關系。主要研究成果發表在Math. Ann., Adv. Math., Comm. Math. Phys., IMRN等期刊上。