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Semi-infinite flags and Zastava spaces

Semi-infinite flags and Zastava spaces

The semi-infinite flag variety of Feigin and Frenkel is an infinite-dimensional generalization

of the ordinary flag variety associated to a reductive group. Although its sheaf theory is

expected to have deep connections with representations of Kac-Moody algebras and quantum

groups, the infinite-dimensional nature of the space has made constructing its category of D-

modules a difficult task. I will review an early construction of the category using spaces of

based maps from the projective line into the ordinary flag variety (aka ”Zastava spaces”), as

well as a recent construction by Gaitsgory via the semi-infinite intersection cohomology sheaf

on the affine Grassmannian. Following that, I will explain how to modify the geometry of

the Zastava space so that its ordinary intersection cohomology sheaf becomes equivalent, in a

sense which I will make precise, to the semi-infinite IC sheaf.

## Department of Mathematics and Statistics