Metaplectic Whittaker category and quantum groups : the "small" FLE

2019/03/06 by Dennis Gaitsgory, Gaitsgory, D., S. D. Lysenko +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1903.02279

openalex publication_date 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the category of Hecke eigensheaves in the metaplectic Whittaker category of the affine Grassmannian is equivalent to the category of modules over the small quantum group. This a step towards proving the FLE: the fundamental local equivalence in the quantum geometric Langlands theory.

Citations

• Sheaves of categories and the notion of 1-affineness

Cited by

• Modular intersection cohomology of Drinfeld's compactifications

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