A "strange" functional equation for Eisenstein series and miraculous duality on the moduli stack of bundles

TL;DR

This paper introduces a novel duality functor on D-modules over the moduli stack of bundles, arising from the failure of Verdier duality, and explores its connection to Eisenstein series.

Contribution

It presents a new duality framework for D-modules on Bun(G) linked to Eisenstein series, addressing a fundamental duality failure.

Findings

New duality functor on D-modules on Bun(G)

Relation established between duality and Eisenstein series

Insights into the failure of Verdier duality

Abstract

We show that the failure of the usual Verdier duality on Bun(G) leads to a new duality functor on the category of D-modules, and we study its relation to the operation of Eisenstein series.