报告题目(Title)：Quantum vertex algebras and their representations(量子顶点代数及其表示)

报告人(Speaker)：Prof.Slaven Kozic (克罗地亚萨格勒布大学)

报告时间(Time)：2022年12月3日(周六) 20:00

报告地点(Place)：腾讯会议（会议号：177-279-995）

邀请人(Inviter)：张红莲、孙建才

主办部门：理学院数学系

报告摘要：One important problem in the vertex algebra theory is to associate certain vertex algebra-like objects, the so-called quantum vertex algebras, to various classes of quantum groups, such as quantum affine algebras or double Yangians. Roughly speaking, the goal is to establish a correspondence between these structures that goes in parallel with the already established connection between affine Kac-Moody Lie algebras and vertex algebras. In this talk, I will discuss this problem in the context of Etingof-Kazhdan's quantum vertex algebra associated with the trigonometric R-matrix in type A. More specically, in this setting, the usual notion of (quantum) vertex algebra module does no longer seem to be suitable, so we use Li's notion of phi-coordinated module instead. This allows us to prove that a certain broad class of modules for the (suitably completed) quantum affine algebra in type A coincides with the class of phi-coordinated modules for the aforementioned quantum vertex algebra.