This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.
Geometric Eisenstein series
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abstract
The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of parabolic bundles on a curve suggested by V.Drinfeld. As an application we construct certain automorphic forms for global fields of positive characteristic, whose existence is non-obvious from the point of view of classical tools.
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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.