BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Keyu Wang (Paris Cité) DTSTART:20230206T130000Z DTEND:20230206T140000Z DTSTAMP:20260710T042710Z UID:paris-algebra-seminar/122 DESCRIPTION:Title: QQ˜ -systems for twisted quantum affine algebras\nby Keyu Wang (Paris Cité) as part of Paris algebra seminar\n\n\nAbstract\nAs a part of Langlands duality\, certain equations were found in two differe nt areas of mathematics. They are known as Baxter’s TQ systems and the Q Q type systems\, as they trace back to Baxter’s study on integrable mode ls in the 1970s. During the same decade\, similar systems of equations wer e discovered in the area of ordinary differential equations (ODE) by Sibuy a\, Voros and others. Today\, this remarkable correspondence is realized a s a duality between representation theory of nontwisted quantum affine alg ebras (QAA) and the theory of opers for their Langlands dual Lie algebras. \n\nWe are interested in this duality when the roles of the affine Lie alg ebra and its dual are exchanged. When the nontwisted QAA is of type BCFG\, its dual will be a twisted QAA. To exchange their roles amounts to studyi ng representations of twisted QAAs.\n\nIn this talk\, we will begin by rev iewing this story. We will explain the representation theory of twisted QA As and their Borel algebras. We will explain the expected relationship bet ween twisted and nontwisted types\, and we will establish TQ systems and Q Q^{~} systems for twisted QAAs.\n\nThis talk will take place in hybrid mod e at the IHP.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/122/ END:VEVENT END:VCALENDAR