On some development of unitary representations of reductive Lie groups
蔡宛育教授中原大學應用數學系 15:30 – 17:00 鴻經館 M107
Abstract：
In this talk, we sketch the historical development of representation theory of reductive Lie groups, especially on the progress of solving the unitary dual problem. We will discuss this by first talking about finite groups, and then compact Lie groups and reductive Lie groups. Some major problems that have been solved for linear Lie groups are still mysterious for nonlinear Lie groups. We then discuss the growing importance of studying genuine representations of the nonlinear double cover of a real reductive Lie group. In particular, we are interested in the classification of genuine small representations and the algebraic properties that they carry. These small representations are part of the building blocks of the unitary dual of a nonlinear covering group, and have lots of applications in number theory.