重新探讨Salamanca-Riba与Vogan的一个猜想



活动地点:腾讯会议

活动时间:2022-09-15 14:00:00

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vn99威尼斯人手机版数学系

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.

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