Nilpotent matrix and finite W-(super)algebra

发布时间：2022-04-01 作者：浏览次数：

Speaker:	彭勇寜	DateTime:	2022年4月6日(周三) 下午2：00-3：00
Brief Introduction to Speaker: 彭勇寜，教授，台湾中央大学数学系		Place:	腾讯会议：764137987(密码 2246)
Abstract: Finite W-algebra, which is essentially determined by a nilpotent element in a simple or reductive Lie algebra, can be viewed as a refinement of the universal enveloping algebra. It has appeared in many different fields of mathematics, possibly with different terminologies. The study of W-algebra can be traced back to Kostant's classic works on nilpotent orbits around 1980's. It has being studied intensively since Premet's works on Slodowy slices around 2000's, where the modern terminologies are introduced. In this talk, we will focus on the type A case: starting from a nilpotent matrix, we explain how the associated W-algebra is defined, and then introduce a realization of W-algebra estab- lished by Brundan-Kleshchev, in terms of some algebraic structure called shifted Yangian. Finally we will mention a recent generalization of this realization to the case of general linear Lie superalgebra.