»ã±¨±êÌâ (Title)£ºRevisiting a conjecture of Salamanca-Riba and Vogan (³ÁÐÂ̽ÇóSalamanca-RibaÓëVoganµÄÒ»¸ö²Â²â)

»ã±¨ÈË (Speaker)£º»Æ¼ÒÔ£ ÖúÀí½ÌÊÚ (Ïã¸ÛÖÐÎÄ´óѧ(ÉîÛÚ))

»ã±¨¹¦·ò (Time)£º2022Äê09ÔÂ15ÈÕ(ÖÜËÄ) 14:00-15:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé £¨»áÒé ID£º438-108-860£©

Ô¼ÇëÈË(Inviter)£ººÎº£°²

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»ã±¨ÌáÒª£ºOne 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.