BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dan Ciubotaru (Oxford University) DTSTART:20211208T210000Z DTEND:20211208T220000Z DTSTAMP:20260423T052329Z UID:MITLie/45 DESCRIPTION:Title: A nonabelian Fourier transform for tempered unipotent representations of p -adic groups\nby Dan Ciubotaru (Oxford University) as part of MIT Lie groups seminar\n\nLecture held in The Simons Building in Room: 2-142.\n\nA bstract\nIn the representation theory of finite reductive groups\, an esse ntial role is played by Lusztig's nonabelian Fourier transform\, an involu tion on the space of unipotent characters the group. This involution is th e change of bases matrix between the basis of irreducible characters and t he basis of `almost characters'\, certain class functions attached to char acter sheaves. For reductive p-adic groups\, the unipotent local Langlands correspondence gives a natural parametrization of irreducible smooth repr esentations with unipotent cuspidal support. However\, many questions abou t the characters of these representations are still open. Motivated by the study of the characters on compact elements\, we introduce in joint work with A.-M. Aubert and B. Romano (arXiv:2106.13969) an involution on the sp aces of elliptic and compact tempered unipotent representations of pure in ner twists of a split simple p-adic group. This generalizes a construction by Moeglin and Waldspurger (2003\, 2016) for elliptic tempered representa tions of split orthogonal groups\, and potentially gives another interpret ation of a Fourier transform for p-adic groups introduced by Lusztig (2014 ). We conjecture (and give supporting evidence) that the restriction to re ductive quotients of maximal compact open subgroups intertwines this invol ution with a disconnected version of Lusztig's nonabelian Fourier transfor m for finite reductive groups.\n LOCATION:https://researchseminars.org/talk/MITLie/45/ END:VEVENT END:VCALENDAR