Deligne--Lusztig duality on the moduli stack of bundles

Abstract

Let $Bu{n}_G(X)$ be the moduli stack of $G$-torsors on a smooth projective curve $X$ for a reductive group $G$. We prove a conjecture made by Drinfeld-Wang and Gaitsgory on the Deligne-Lusztig duality for D-modules on $Bu{n}_G(X)$. This conjecture relates Drinfeld-Gaitsgory's pseudo-identity functors to the enhanced Eisenstein series and geometric constant term functors on $DMod(Bu{n}_G(X))$. We also prove a "second adjointness" result for these enhanced functors.

arXiv comment52 pages; correction of typos; small modification of structure

References in corpus (5)

• Higher Topos Theory
• On algebraic spaces with an action of G_m
• On an invariant bilinear form on the space of automorphic forms via asymptotics
• On the reductive monoid associated to a parabolic subgroup
• Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groups

Cited by in corpus (1)

• Duality for automorphic sheaves with nilpotent singular support