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SUMMARY:Syu Kato: Frobenius splitting of semi-infinite flag manifolds
DTSTART:20190206T020000Z
DTEND:20190206T030000Z
DTSTAMP:20241015T052100Z
UID:indico-session-632@indico.ipmu.jp
DESCRIPTION:We explain that extremal weight modules of quantum loop algebr
as give rise to the projective coordinate ring of the formal model of the
semi-infinite flag manifolds over the ring of integers with two inverted.
Then\, we exhibit how this gives rise to the Frobenius splitting of such a
n (ind-)scheme. This particularly implies that the Schubert varieties of t
he quasi-map spaces from a projective line to a (partial) flag manifold ad
mits a Frobenius splitting compatible with the boundaries\, and consequent
ly such varieties are normal and has rational singularity in characteristi
c zero. This extends the case of the genuine quasi-map spaces by Braverman
-Finkelberg and the asymptotic case by myself.\n\nIf time allows\, we expl
ain how to use such results to understand the structure of equivariant sma
ll quantum $K$-theory of a (partial) flag manifold.\n\nhttps://indico.ipmu
.jp/event/168/sessions/632/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
RELATED-TO:indico-event-168@indico.ipmu.jp
URL:https://indico.ipmu.jp/event/168/sessions/632/
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