BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ivan Losev (Yale Universiy) DTSTART:20210224T213000Z DTEND:20210224T223000Z DTSTAMP:20260423T003251Z UID:MITLie/21 DESCRIPTION:Title: Unipotent Harish-Chandra bimodules\nby Ivan Losev (Yale Universiy) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nUnip otent representations of semisimple Lie groups is a very important and som ewhat conjectural class of unitary representations. Some of these represen tations for complex groups (equivalently\, Harish-Chandra bimodules) were defined in the seminal paper of Barbasch and Vogan from 1985 based on idea s of Arthur. From the beginning it was clear that the Barbasch-Vogan const ruction doesn't cover all unipotent representations. The main construction of this talk is a geometric construction of Harish-Chandra bimodules that should exhaust all unipotent bimodules. A nontrivial result is that all u nipotent bimodules in the sense of Barbasch and Vogan are also unipotent i n our sense. The proof of this claim is based on the so called symplectic duality that in our case upgrades a classical duality for nilpotent orbits in the version of Barbasch and Vogan. Time permitting I will explain how this works. The talk is based on a joint work with Lucas Mason-Brown and D mytro Matvieievskyi.\n LOCATION:https://researchseminars.org/talk/MITLie/21/ END:VEVENT END:VCALENDAR