Parabolic geometric Eisenstein series and constant term functors

TL;DR

This paper establishes compatibility and structural relations between geometric Eisenstein series, Whittaker sheaves, and constant term functors within the geometric Langlands framework, extending previous results and introducing new dualities.

Contribution

It introduces new Hecke structures on geometric Eisenstein series and relates compactified and non-compactified series via Koszul duality, advancing understanding of geometric Langlands theory.

Findings

Proves compatibility between parabolic restriction of Whittaker sheaves and representation restriction.

Establishes Hecke structures on geometric Eisenstein series functors, generalizing prior work.

Relates compactified and non-compactified Eisenstein series through Koszul duality.

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.