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SUMMARY:Frobenius splitting of semi-infinite flag manifolds
DTSTART;VALUE=DATE-TIME:20190206T020000Z
DTEND;VALUE=DATE-TIME:20190206T030000Z
DTSTAMP;VALUE=DATE-TIME:20240417T145724Z
UID:indico-contribution-632-2639@indico.ipmu.jp
DESCRIPTION:Speakers: Syu Kato ()\nWe explain that extremal weight modules
of quantum loop algebras give rise to the projective coordinate ring of t
he formal model of the semi-infinite flag manifolds over the ring of integ
ers with two inverted. Then\, we exhibit how this gives rise to the Froben
ius splitting of such an (ind-)scheme. This particularly implies that the
Schubert varieties of the quasi-map spaces from a projective line to a (pa
rtial) flag manifold admits a Frobenius splitting compatible with the boun
daries\, and consequently such varieties are normal and has rational singu
larity in characteristic zero. This extends the case of the genuine quasi-
map spaces by Braverman-Finkelberg and the asymptotic case by myself.\n\nI
f time allows\, we explain how to use such results to understand the struc
ture of equivariant small quantum $K$-theory of a (partial) flag manifold.
\n\nhttps://indico.ipmu.jp/event/168/contributions/2639/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2639/
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