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DTSTART:20250330T030000
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DTSTAMP:20260424T081432Z
UID:648ae9a9a37ab748594650@ist.ac.at
DTSTART:20250716T130000
DTEND:20250716T150000
DESCRIPTION:Speaker: Leonid Rybnikov\nhosted by Tamas Hausel\nAbstract: Let
  g be a complex simple finite-dimensional Lie algebra and G be the adjoint
  Lie group with the Lie algebra g. To every group element C from G\, one c
 an assign a commutative subalgebra B(C) in the Yangian Y(g)\, which is res
 ponsible for the integrals of the (generalized) XXX Heisenberg magnet chai
 n. For regular semisimple C\, the images of Bethe subalgebras in tensor pr
 oducts of fundamental representations are equivariant quantum cohomology r
 ings of Nakajima quiver varieties. We describe the degenerations of Bethe 
 subalgebras in terms of "shift of argument" subalgebras (or big subalgebra
 s) in universal enveloping algebras. Furthermore\, using these degeneratio
 ns\, we construct a natural structure of affine crystals on spectra of B(C
 ) in Kirillov-Reshetikhin g-modules in type A. We conjecture that such a c
 onstruction exists for arbitrary g and gives Kirillov-Reshetikhin crystals
 . The talk is based on joint results with Aleksei Ilin\, Vasily Krylov\, a
 nd Inna Mashanova-Golikova.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Leonid Rybnikov: Bethe subalgebras in Yangians\, their degeneration
 s and crystals
URL:https://talks-calendar.ista.ac.at/events/5918
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