Irreducible unitary representations are building blocks for non-commutative harmonic analysis. A basic problem of representation theory of Lie groups is to construct and classify irreducible unitary representations of real reductive groups. Among all  irreducible unitary representations, the most intriguing ones are the so called unipotent representations associated to nilpotent coadjoint orbits.

After reviewing some basics of representation theory of real reductive groups, we will explain a construction of unipotent representations of classical Lie groups. This is a joint work in progress with Jiajun Ma and Chengbo Zhu.

孙斌勇研究员是表示论方向的国际顶尖学者。他致力于典型群无穷维表示论中重大问题的研究。他和合作者系统研究了不变广义函数理论，并以此为基础解决了典型群无穷维表示论中的一系列重要问题，包括Bernstein-Rallis重数一猜想、Kudla-Rallis守恒律猜想等。孙斌勇研究员于2014年获得陈嘉庚青年科学奖。