Geometric constant term functor(s)

TL;DR

This paper investigates the geometric theory of automorphic functions, establishing a canonical isomorphism between two types of constant term functors associated with parabolic subgroups in the context of D-modules on moduli stacks.

Contribution

It proves that the !-constant term functor is canonically isomorphic to the *-constant term functor for opposite parabolics in the geometric automorphic setting.

Findings

Canonical isomorphism between !- and *-constant term functors

Framework applicable to geometric automorphic functions

Enhances understanding of functorial properties in geometric Langlands

Abstract

We study the Eisenstein series and constant term functors in the framework of geometric theory of automorphic functions. Our main result says that for a parabolic P in G with Levi quotient M, the !-constant term functor CT_!:D-mod(Bun_G)-> D-mod(Bun_M) is canonically isomorphic to the *-constant term functor CT^-_*:D-mod(Bun_G)\to D-mod(Bun_M), taken with respect to the opposite parabolic P^-.