Title1:From conjugate classes of square matrices to smooth representations of classical groups
Time: Mon, Dec. 12, 2016, AM 09:30-10:30
Speaker: Prof. Chengbo Zhu (National University of Singapore  )
Location:Room 4318, Building No.4, Wushan Campus
Abstract: 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.