Deligne--Lusztig duality on the moduli stack of bundles

Lin Chen

Deligne--Lusztig duality on the moduli stack of bundles

Representation Theory 2022-01-25 v4 Algebraic Geometry

Authors: Lin Chen

Abstract

Let $Bun_G(X)$ 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 $Bun_G(X)$ . This conjecture relates Drinfeld-Gaitsgory's pseudo-identity functors to the enhanced Eisenstein series and geometric constant term functors on $DMod(Bun_G(X))$ . We also prove a "second adjointness" result for these enhanced functors.

Keywords

moduli stack deligne-lusztig duality d-modules pseudo-identity functors eisenstein series second adjointness

Cite

@article{arxiv.2008.09348,
  title  = {Deligne--Lusztig duality on the moduli stack of bundles},
  author = {Lin Chen},
  journal= {arXiv preprint arXiv:2008.09348},
  year   = {2022}
}

Comments

52 pages; correction of typos; small modification of structure

Deligne--Lusztig duality on the moduli stack of bundles

Abstract

Keywords

Cite

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