3-8 February 2019
Lecture Hall(1F), Kavli IPMU
Asia/Tokyo timezone

Frobenius splitting of semi-infinite flag manifolds

6 Feb 2019, 11:00
Lecture Hall(1F), Kavli IPMU

Lecture Hall(1F), Kavli IPMU


Syu Kato


We explain that extremal weight modules of quantum loop algebras 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 an (ind-)scheme. This particularly implies that the Schubert varieties of the quasi-map spaces from a projective line to a (partial) flag manifold admits a Frobenius splitting compatible with the boundaries, and consequently such varieties are normal and has rational singularity in characteristic zero. This extends the case of the genuine quasi-map spaces by Braverman-Finkelberg and the asymptotic case by myself.

If time allows, we explain how to use such results to understand the structure of equivariant small quantum $K$-theory of a (partial) flag manifold.

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