报告时间：2021年3月11日  10:00-11:00

报告地点： 精正楼二楼报告厅

报告人：马家骏 (上海交通大学)

报告摘要：

In this talk, I will discuss the recent work joint with Dan Barbasch, Binyong Sun, and Chengbo Zhu on the construction and (combinatorial) classification of special unipotent representations of real classical groups (including real/quaternionic symplectic/orthogonal groups and metaplectic groups). Special unipotent representations are certain irreducible admissible representations attached to the unipotent in the Langlands dual group. They are conjectured to be unitarizable and to form the unipotent Arthur packet. Barbasch and Vogan (1985) established the theory of special unipotent representations for complex reductive groups (construction, unitarizability, character formula, etc.).

Using theta correspondence, we will construction all unipotent representations attached to nilpotent orbits with good parity and show they are all unitarizable. Besides, we can compute the associated characters and degenerate Whittaker models of these representations. Special unipotent representations attached to general nilpotent orbits can be constructed via irreducible parabolic inductions from the good parity ones. In particular, we settle the conjecture mentioned above.

Some examples will be discussed through the talk.

欢迎参加！

邀请人：白占强, 董超平