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

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arxiv 1903.02279 v1 pith:AMQREET4 submitted 2019-03-06 math.AG

D. Gaitsgory , S. Lysenko This is my paper · ORCID
classification math.AG
keywords categoryquantummetaplecticsmallwhittakeraffineeigensheavesequivalence
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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.

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Cited by 3 Pith papers

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  1. Parabolic geometric Eisenstein series and constant term functors

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    This paper proves that parabolic Jacquet functors on Whittaker categories match restriction and Lie algebra cohomology of representations under the geometric Casselman-Shalika equivalence.

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  3. Note on factorization categories

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