This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.
Contractibility of the space of rational maps
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abstract
We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space Bun(G) of G-bundles on X is uniformized by the appropriate rational version of the affine Grassmannian, where the uniformizing map has contractible fibers.
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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.