校 级 学 术 报 告
法国巴黎高师数学系David Hernandez教授是国际上从事仿射型量子群的表示论的新秀，他在Chari- Pressely-Frenkel-Reshetikhin 创立的有限维表示论及q-t-特征标理论方面作出了系列的重要工作，其中解决了Frenkel-Reshetikhin的有名猜想。量子群理论直接发端于统计物理和理论物理的Yang-Baxter方程的求解理论，与李代数、代数群、Hopf代数、3流形的扭结不变量理论、非交换几何领域等有直接的联系，也是物理学家关注的重要方面之一。量子群的发展目前已深入到现代数学的各个部门和领域，是当前备受国际数学家和数学物理学家瞩目的热门研究领域。David Hernandez将就他最近的新研究成果作学术报告。
Quantum Fusion Tensor Category and Generalized T-Systems
The Drinfeld ``coproduct'' of a quantum affinization, for example of a quantum affine algebra or a quantum toroidal algebra (which has no Hopf algebra structure), does not produce tensor products of modules in the usual way because it is defined in a completion. In this talk we present a new process to produce quantum fusion modules from it : for all quantum affinizations we construct by deformation a (non semi-simple) tensor category. We will discuss several applications : we construct the fusion of any l-highest weight modules, and prove that it is always cyclic. In particular a simple module is a quotient of a fusion of fundamental representations. We establish exact sequences involving fusion of Kirillov-Reshetikhin modules related to new T-systems.
欢迎数学系、物理系的广大师生前来听讲！
时间：6月30日上午10：00---11：00
地点：理科大楼510室
