BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeffrey Adams (University of Maryland) DTSTART:20220915T143000Z DTEND:20220915T160000Z DTSTAMP:20260422T150051Z UID:atlas/37 DESCRIPTION:Title: C ohomological Arthur Packets 2\nby Jeffrey Adams (University of Marylan d) as part of Real reductive groups/atlas\n\n\nAbstract\n(This is a contin uation of the talk from last week)\n\nAn important special case of Arthur packets are those of regular integral infinitesimal character. The trivial representation (attached to the dual principal nilpotent orbit) is an exa mple. \n\nIt is known by a result of Salamanca that the unitary representa tions with regular integral infinitesimal character are precisely the coho mological representations. These are representations with non-trivial twis ted $(\\mathfrak g\,K)$ cohomology. By a result of Vogan and Zuckerman the se are precisely the modules $A_\\mathfrak q(\\lambda)$\, constructed via cohomological induction from a unitary character of theta-stable Levi subg roup. \n\nThe conclusion is: assuming all is right with the world (i.e. Ar thur's conjectures) an Arthur packet consisting of representations with re gular integral infinitesimal character\nmust consist of certain $A_\\mathf rak q(\\lambda)$-modules. These are sometimes referred to as "Adams-Johnso n" packets\; these were among the first interesting Arthur packets to be s tudied in the 1980s.\n\nI'll discuss these things in the context of Atlas. \n LOCATION:https://researchseminars.org/talk/atlas/37/ END:VEVENT END:VCALENDAR