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Abstract: 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. For classical Lie groups, we construct some irreducible unitary representations attached to nilpotent coadjoint orbits, by using the theory of local theta correspondence initiated by R. Howe. These are the special unipotent representations in the sense of Arthur and Barbasch-Vogan. This is a report on a recent joint work with Dan M. Barbarsch, Jia-Jun Ma and Chen-Bo Zhu.
Bio: 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. After a short postdoctoral experience at the Swiss Federal Institute of Technology Zurich, he worked at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences since 2005. In 2020, he then joined the Institute for Advanced Study in Mathematics (IASM) at Zhejiang University as a permanent member.
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 a member of the Chinese Academy of Sciences.
