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SUMMARY:Equivariant multiplicities via representations of quantum affine a
 lgebras - Elie Casbi (Max-Planck-Institut für Mathematik\, Bonn)
DTSTART:20211122T160000Z
DTEND:20211122T170000Z
UID:TALK166207@talks.cam.ac.uk
DESCRIPTION:&nbsp\;Equivariant multiplicities via representations of quant
 um affine algebrasElie CasbiFor any simply-laced type simple Lie algebra g
  and any height function &xi\; adapted to anorientation Q of the Dynkin di
 agram of g\, Hernandez-Leclerc introduced a certain categoryC&frasl\;&xi\;
  of representations of the quantum affine algebra Uqppgq\, as well as a su
 bcategory CQ ofC&frasl\;&xi\; whose complexified Grothendieck ring is isom
 orphic to the coordinate ring CrNs of amaximal unipotent subgroup. In this
  talk\, I will present our construction of an algebraic morphism Dr&xi\; o
 n a torus Y&frasl\;&xi\; containing the image of K0pC&frasl\;&xi\;q under 
 the truncated q-charactermorphism. We prove that the restriction of Dr&xi\
 ; to K0pCQq coincides with the morphism D recently introduced by Baumann-K
 amnitzer-Knutson in their study of equivariant multiplicitiesof Mirković-
 Vilonen cycles. I will begin by showing how the cluster structure of CrNs 
 playeda key role in the proof of this result. I will also explain how this
  alternative description of Dallowed us to prove a conjecture from an earl
 ier work of mine on the distinguished values ofD on the flag minors of CrN
 s. Finally I will conclude with some applications of our resultsand some p
 erspectives of further developments.This is a joint work with Jianrong LI.
 &nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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