This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.
Semi-infinite parabolic IC-sheaf
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abstract
Let G be a connected reductive group, P its parabolic subgroup. We consider the parabolic semi-infinite category of sheaves on the affine Grassmanian of G and construct the parabolic version of the semi-infinite IC-sheaf of each orbit. We establish some of its properties and relate it to sheaves on the Drinfeld compactification of the moduli stack Bun_P of P-torsors on a curve. We also relate the parabolic semi-infinite IC-sheaf with the dual baby Verma object on the spectral side.
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Parabolic geometric Eisenstein series and constant term functors
This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.