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arXiv · 2507.13930

Parabolic geometric Eisenstein series and constant term functors

Joakim Faergeman·Andreas Hayash
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Abstract

We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we establish various Hecke structures on geometric Eisenstein series functors, generalizing results of Braverman-Gaitsgory in the case of a principal parabolic. Moreover, we relate compactified and non-compactified geometric Eisenstein series functors via Koszul duality. We sketch a proof that the spectral-to-automorphic geometric Langlands functor commutes with constant term functors.

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Joakim Faergeman, Andreas Hayash. 2025-07-18. Parabolic geometric Eisenstein series and constant term functors. https://arxiv.org/abs/2507.13930

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