BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vasily Krylov (MIT Mathematics) DTSTART:20210414T203000Z DTEND:20210414T213000Z DTSTAMP:20260423T052448Z UID:MITLie/27 DESCRIPTION:Title: Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric Satake equivalence\nby Vasily Krylov (MIT Mathematics) as part of MIT Lie gr oups seminar\n\nLecture held in 2-142.\n\nAbstract\nThis talk is based on the paper (joint with M. Finkelberg and I. Mirković).\n\nLet G be a reduc tive complex algebraic group. Recall that a geometric Satake isomorphism i s an equivalence between the category of G(O)-equivariant perverse sheaves on the affine Grassmannian for G and the category of finite dimensional r epresentations of the Langlands dual group \\hat{G}. It follows that for a ny G(O)-equivariant perverse sheaf P there exists an action of the dual Li e algebra \\hat{\\mathfrak{g}} on the global cohomology of P.\n\nWe will e xplain one possible approach to constructing this action. To do so\, we wi ll describe a new geometric construction of the universal enveloping algeb ra of the positive nilpotent subalgebra of the Langlands dual Lie algebra \\hat{\\mathfrak{g}} based on certain one-parametric deformation of zastav a spaces. We will introduce the so-called Drinfeld-Gaitsgory-Vinberg inter polation Grassmannian that is a one-parametric deformation of the affine G rassmannian Gr_G. We will discuss the case G=SL_2 as an example.\n LOCATION:https://researchseminars.org/talk/MITLie/27/ END:VEVENT END:VCALENDAR