Westlake Online Math Forum第五期 | Binyong Sun: Special unipotent representations of classical Lie groups

2023-01-11 09:16:14


ZOOM ID:960 7758 5827

PASSCODE: 312774

主持人: 理论科学研究院 关力凡 博士

主讲人: 浙江大学 孙斌勇 教授

主讲人简介:Binyong Sun received his bachelor's degree from Zhejiang University in 1999, and doctorate degree from the Hong Kong University of Science and Technology in 2004. He worked at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences since 2005. He then joined Zhejiang University in 2020.

Binyong Sun's research interests include representation theory of Lie groups and the theory of automorphic forms. By proving some long-standing conjectures, he has established several deep and fundamental results for representations of classical groups. He received the Tan Kah Kee Young Scientist Award in 2014, the Outstanding Youth Science and Technology Talent Award in 2016, and the State Natural Science Award (second class) in 2018. In 2019, he was elected member of Chinese Academy of Sciences.

讲座主题:Special unipotent representations of classical Lie groups

讲座摘要: One fundamental problem in representation theory is the unitary dual problem, namely to construct and classify all irreducible unitary representations of a given Lie group G. An important principle is the orbit method introduced by A. A. Kirillov, and it seeks to describe irreducible unitary representations of G by its coadjoint orbits. The most mysterious ingredient of orbit method is to attach irreducible unitary representations to nilpotent coadjoint orbits. Special unipotent representations, introduced by Arthur and Barbasch-Vogan, are attached to nilpotent coadjoint orbits and are expected to be unitary. By using the theory of local theta correspondence initiated by R. Howe, we construct all special unipotent representations of classical Lie groups and show that they are all unitary. This is a report on a joint work with Dan M. Barbarsch, Jia-Jun Ma and Chen-Bo Zhu.