Tensor structures on representation categories of Lie algebras
劉佳澄先生加拿大多倫多大學數學系博士生 下午 2:30–4:00 鴻經館 107 室We will introduce a non-standard braided tensor structure on the category of finite dimensional representations of a complex simple Lie algebra, first defined by Drinfeld by means of the Knizhnik-Zamolodchikov equations in 1990. This category is also closely related to the representation theory of the corresponding affine Lie algebra. In particular, following Kazhdan and Lusztig's remarkable result in 1994, we should really think of Drinfeld's category as a certain representation category of the affine Lie algebra, equipped with a nontrivial tensor structure. In this talk, we will try to explain how the Knizhnik-Zamolodchikov equations and affine Lie algebras naturally appear in this story.