BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Vogan (MIT Mathematics) DTSTART:20200909T203000Z DTEND:20200909T213000Z DTSTAMP:20260423T021041Z UID:MITLie/7 DESCRIPTION:Title: S tructure of Harish-Chandra cells\nby David Vogan (MIT Mathematics) as part of MIT Lie groups seminar\n\n\nAbstract\nOne of the fundamental contr ibutions of Kazhdan and Lusztig's 1979 Inventiones paper was the notion of "cells" in Weyl groups. They gave a decomposition of the left regular rep resentation of W as a direct sum of "left cell" representations\, which en code deep and powerful information about group representations. In the cas e of the symmetric group S_n=W\, the left cells are irreducible representa tions. In all other cases they are not. Lusztig in his 1984 book gave a be autiful description of all left cells in terms of the geometry of a nilpot ent orbit.\n\\\\\nThere is a parallel notion of "Harish-Chandra cells" in the representation theory of a real reductive group G(R). Again each cell is a representation of W\, encoding deep information about the G(R) repres entations. I will formulate a conjecture extending Lusztig's calculation o f left cell representations to this case\, and explain its connection with Arthur's theory of unipotent representations.\n LOCATION:https://researchseminars.org/talk/MITLie/7/ END:VEVENT END:VCALENDAR