This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.
Langlands duality on the Beilinson-Drinfeld Grassmannian
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abstract
We calculate various categories of equivariant sheaves on the Beilinson-Drinfeld Grassmannian in Langlands dual terms. For one, we obtain the factorizable derived geometric Satake theorem. More generally, we calculate the categorical analogue of unramified vectors in the Jacquet module of sheaves on the Grassmannian. In all cases, our spectral categories involve factorization modules for factorization algebras related to the Langlands dual group.
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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.