Chiral Principal Series Categories I: Finite Dimensional Calculations
نویسنده
چکیده
This paper begins a series studying D-modules on the Feigin-Frenkel 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 Braverman-Gaitsgory. Moreover, we compare this geometric realization of the Langlands dual group to the standard one provided by (factorizable) geometric Satake.
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