BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georgy Sharygin DTSTART:20250402T162000Z DTEND:20250402T180000Z DTSTAMP:20260423T023020Z UID:GDEq/131 DESCRIPTION:Title: T he quantum argument shift method on $U\\mathfrak{gl}_n$\nby Georgy Sha rygin as part of Geometry of differential equations seminar\n\nLecture hel d in room 303 of the Independent University of Moscow.\n\nAbstract\nThe te rm "argument shift method" is used for a simple and efficient method to co nstruct commutative subalgebras in Poisson algebras by deforming the Casi mir elements in them. This method is primarily used to search for Poisson commutative subalgebras in symmetric algebras of various Lie algebras\; i t is closely related with the bi-Hamiltonian induction (Lenard-Magri schem e). However little is known about the possible extension of this method t o the quantum algebras associated with given Poisson algebras\; this is tr ue even for the symmetric algebra of a Lie algebra\, where the quantizati on is well known (it is equal to the universal enveloping algebra). I will tell about a particular case\, the algebra $U\\mathfrak{gl}_n$\, for whi ch one can find a shifting operator raising to this algebra the shift on  $S(\\mathfrak{gl}_n)$\, and prove that this operator verifies the same c ondition as before: when used to deform the elements in the center of $U\ \mathfrak{gl}_n$\, it yields a set of commuting elements.\n\nThe talk is p artially based on joint works with Y.Ikeda.\n LOCATION:https://researchseminars.org/talk/GDEq/131/ END:VEVENT END:VCALENDAR