Chiral principal series categories I: Finite dimensional calculations

This paper begins a series studying D-modules on the FeiginFrenkel semi-infinite flag variety from the perspective of the Beilinson-Drinfeld factorization (or chiral) theory. Here we calculate Whittaker-twisted cohomology groups of Zastava spaces, which are certain finite-dimensional subvarieties of the affine Grassmannian. We show that such cohomology groups realize the nilradical of a Borel subalgebra for the Langlands dual group in a precise sense, following earlier work of Feigin-Finkelberg-Kuznetsov-Mirkovic and BravermanGaitsgory. Moreover, we compare this geometric realization of the Langlands dual group to the standard one provided by (factorizable) geometric Satake. (c) 2021 Published by Elsevier Inc.

Automated summary

This paper initiates a study of D-modules on the FeiginFrenkel semi-infinite flag variety using the Beilinson-Drinfeld factorization theory. By calculating Whittaker-twisted cohomology groups of Zastava spaces, certain finite-dimensional subvarieties of the affine Grassmannian, it is shown that these cohomology groups realize the nilradical of a Borel subalgebra for the Langlands dual group in a precise sense. This geometric realization of the Langlands dual group is compared to the standard one provided by (factorizable) geometric Satake.