Langlands duality on the Beilinson-Drinfeld Grassmannian

2023/10/30 by Justin Campbell, Campbell, Justin, Sam Raskin +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2310.19734

openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate various categories of equivariant sheaves on the Beilinson-Drinfeld Grassmannian in Langlands dual terms. For one, we obtain the factorizable derived geometric Satake theorem. More generally, we calculate the categorical analogue of unramified vectors in the Jacquet module of sheaves on the Grassmannian. In all cases, our spectral categories involve factorization modules for factorization algebras related to the Langlands dual group.

Cited by

• Isotopy invariance and stratified 𝔼₂-structure of the Ran Grassmannian
• Modular intersection cohomology of Drinfeld's compactifications

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