学术报告 报告题目：From conjugate classes of square matrices to smooth representations of classical
groups
报 告 人：朱程波 教授（新加坡国立大学）
报告时间：2016年12月12日（星期一）上午09:30-10:30
报告地点：4号楼4131室
欢迎广大师生前往！
数学学院
2016年12月07日
报告摘要：
From thebeginning of representation theory near the end of the nineteenth century, it has been a common knowledge that conjugate classes of a group carry critical information about
representations of the group. For a Lie group an elaboration of this idea is called the orbit method, first introduced by A.A. Kirillovin the 1960’s for nilpotent Lie groups and more
recently expounded by D. Vogan for reductive Lie groups, which aims for a tight link between irreducible unitary representations and coadjoint orbits.
This talk is about smooth representations of classical groups with a similar message that
geometry of conjugate classes and their interrelations have important consequences for their representation theory. I will examine two fun facts from linear algebra (conjugacy of A with
A^t, and the relationship of AB with BA, for matrices A, B of sizes m x n and n x m) and then discuss related phenomena on branching rules and singularitiesof infinite-dimensional
representations.