报告题目 (Title)：Revisiting a conjecture of Salamanca-Riba and Vogan (重新探讨Salamanca-Riba与Vogan的一个猜想)

报告人 (Speaker)：黄家裕 助理教授 (香港中文大学(深圳))

报告时间 (Time)：2022年09月15日(周四) 14:00-15:00

报告地点 (Place)：腾讯会议 （会议 ID：438-108-860）

邀请人(Inviter)：何海安

主办部门：理学院数学系

报告摘要：One major unsolved problem in real reductive Lie groups is the classification of the unitary dual. In their 1998 Annals paper, Salamanca-Riba and Vogan proposed that one can reduce the classification problem to Hermitian representations $\pi$ with unitarily small lowest K-types. Their reduction relies on a(n unproved) non-unitarity conjecture involving the infinitesimal character of $\pi$.

In this talk, we propose a sharper non-unitarity conjecture, which immediately implies the conjecture of Salamanca-Riba and Vogan. We will sketch a proof of the refined conjecture for $GL(n,C)$. One expects that similar techniques can be applied to other groups.