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Geometric Eisenstein series

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arxiv math/9912097 v2 pith:ZB5ID7TR submitted 1999-12-12 math.AG math.RT

A.Braverman , D.Gaitsgory This is my paper · ORCID
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keywords certaineisensteingeometricseriesapplicationautomorphicbundlescharacteristic
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The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of parabolic bundles on a curve suggested by V.Drinfeld. As an application we construct certain automorphic forms for global fields of positive characteristic, whose existence is non-obvious from the point of view of classical tools.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parabolic geometric Eisenstein series and constant term functors

    math.RT 2025-07 conditional novelty 8.0 of 10

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

  2. Nonabelian shift operators and shifted Yangians

    math.AG 2024-12 conditional novelty 6.0 of 10

    New nonabelian shift operators and wall-crossing identities show that the quantized Coulomb branch of pure GL_n gauge theory is a quotient of the shifted Yangian Y_{-nα}(sl2), with vertex functions as Hecke eigenfunctions.

  3. Coulomb Branches in 3d $\mathcal{N} = 4$ Revisited

    hep-th 2024-12 conditional novelty 6.0 of 10

    Dual boundary conditions reduce Omega-deformed 3d N = 4 localization to integrals over Hecke modification spaces, recovering the BFN Coulomb branch algebra, boundary modules, and cylindrical KLRW algebras.

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