BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeffrey Adams\, David Vogan (MIT) DTSTART:20221117T153000Z DTEND:20221117T170000Z DTSTAMP:20260422T150327Z UID:atlas/47 DESCRIPTION:Title: M ore about Arthur packets\nby Jeffrey Adams\, David Vogan (MIT) as part of Real reductive groups/atlas\n\n\nAbstract\nBegin with Jeffrey talking about how a weak unipotent Arthur packet for G2 contains two non-unipotent Arthur packets (as constructed by Adams and Johnson in 1987). These stran ge overlaps account for the extra stable sums of irreducibles in the weak packet\, which were displayed last week.\n\nProbably David will then talk about this: if the SL(2) portion of an Arthur parameter psi is not disting uished in the dual group\, then the Bala-Carter Levi L^vee for the SL(2) i s a PROPER Levi. Of course a Levi L^\\vee in G^\\vee corresponds to a Levi L in G\, and this Levi comes with an inner class of rational forms (altho ugh it need NOT be the Levi of a rational parabolic). The Arthur parameter psi for G can be regarded as an Arthur parameter for L. In the real case\ , there are well-behaved "cohomological induction functors" carrying repre sentations of (these rational forms of) L to representations of (our inner class of) rational forms of G. \n\nTHESE INDUCTION FUNCTORS CARRY THE ART HUR PACKET Pi_psi(L) INTO THE ARTHUR PACKET Pi_psi(G).\n\nCONJECTURE: they are ONTO.\n\nIf this is true\, then Arthur packets are only difficult whe n the SL(2) part is DISTINGUISHED\; that is\; the nilpotent is rather larg e\; that is\; the representations are rather far from tempered.\n LOCATION:https://researchseminars.org/talk/atlas/47/ END:VEVENT END:VCALENDAR