Unitary small representations of nonlinear Lie groups
蔡宛育教授中原大學應用數學系 10:30 – 12:00 鴻經館 M107
Abstract：
Minimal representations of reductive groups have been studied for long time and are of significant importance in number theory. The most famous example is the Weil representation of the metaplectic double cover of the symplectic group, which plays a pivotal role in automorphic form and theta correspondence. In this talk, we will first discuss some history of the development of representation theory of reductive groups. Then, more specifically, we will discuss non-minimal small representations arising from a nonlinear double cover of various real reductive groups. We will study some algebraic properties that characterize these small representations. These small representations are expected to be part of the building blocks of unitary representations. The talk is based on some recent results appearing in my papers and joint work with Dan Barbasch.