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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Equivariant multiplicities via representations of
quantum affine algebras - Elie Casbi (Max-Planck-I
nstitut für Mathematik\, Bonn)
DTSTART;TZID=Europe/London:20211122T160000
DTEND;TZID=Europe/London:20211122T170000
UID:TALK166207AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/166207
DESCRIPTION: \;Equivariant multiplicities via representati
ons of quantum affine algebrasElie CasbiFor any si
mply-laced type simple Lie algebra g and any heigh
t function &xi\; adapted to anorientation Q of the
Dynkin diagram of g\, Hernandez-Leclerc introduce
d a certain categoryC&frasl\;&xi\; of representati
ons of the quantum affine algebra Uqppgq\, as well
as a subcategory CQ ofC&frasl\;&xi\; whose comple
xified Grothendieck ring is isomorphic to the coor
dinate ring CrNs of amaximal unipotent subgroup. I
n this talk\, I will present our construction of a
n algebraic morphism Dr&xi\; on a torus Y&frasl\;&
xi\; containing the image of K0pC&frasl\;&xi\;q un
der the truncated q-charactermorphism. We prove th
at the restriction of Dr&xi\; to K0pCQq coincides
with the morphism D recently introduced by Baumann
-Kamnitzer-Knutson in their study of equivariant m
ultiplicitiesof Mirković-Vilonen cycles. I will be
gin by showing how the cluster structure of CrNs p
layeda key role in the proof of this result. I wil
l also explain how this alternative description of
Dallowed us to prove a conjecture from an earlier
work of mine on the distinguished values ofD on t
he flag minors of CrNs. Finally I will conclude wi
th some applications of our resultsand some perspe
ctives of further developments.This is a joint wor
k with Jianrong LI. \;
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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