BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adam Brown (IST\, Austria) DTSTART:20201017T153000Z DTEND:20201017T160000Z DTSTAMP:20260418T110731Z UID:MRTC2020/7 DESCRIPTION:Title: Unitary representations of GL(n) and the geometry of Langlands parameters \nby Adam Brown (IST\, Austria) as part of The 2020 Paul J. Sally\, Jr . Midwest Representation Theory Conference\n\n\nAbstract\nHarish-Chandra's Lefschetz principle suggests that representations of real and p-adic spli t reductive groups are closely related\, even though the methods used to s tudy these groups are quite different. The local Langlands correspondence indicates that these representation theoretic relationships stem from geom etric relationships between real and p-adic Langlands parameters. In this talk\, we will discuss how the geometric structure of real and p-adic Lang lands parameters lead to functorial relationships between representations of real and p-adic groups. I will describe work in progress\, joint with P eter Trapa\, which applies this functoriality to the study of unitary repr esentations and signatures of invariant hermitian forms\, for GL(n). The r esult expresses signatures of invariant hermitian forms on graded affine H ecke algebra modules in terms of signature characters of Harish-Chandra mo dules\, which are computable via the unitary algorithm for real reductive groups by Adams–van Leeuwen–Trapa–Vogan.\n LOCATION:https://researchseminars.org/talk/MRTC2020/7/ END:VEVENT END:VCALENDAR