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Relative Langlands Duality

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arxiv 2409.04677 v1 pith:QHC2JIZ2 submitted 2024-09-07 math.RT math.NTmath.QA

David Ben-Zvi , Yiannis Sakellaridis , Akshay Venkatesh This is my paper · ORCID
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keywords dualitycheckgrouphamiltonianlanglandsrelativespaceanalog
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abstract

We propose a duality in the relative Langlands program. This duality pairs a Hamiltonian space for a group $G$ with a Hamiltonian space under its dual group $\check{G}$, and recovers at a numerical level the relationship between a period on $G$ and an $L$-function attached to $\check{G}$; it is an arithmetic analog of the electric-magnetic duality of boundary conditions in four-dimensional supersymmetric Yang-Mills theory.

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Forward citations

Cited by 5 Pith papers

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

  1. On the cubic Shimura lift to $PGL(3)$: Hecke correspondences

    math.NT 2025-07 conditional novelty 8.0 of 10

    Matching of relative orbital integrals on PGL(3) and metaplectic orbital integrals on the triple cover of SL(3) is established for the full spherical Hecke algebras.

  2. Diagonal cycles on Shtukas and the adjoint $L$-function

    math.NT 2026-07 conditional novelty 7.0 of 10

    For split almost simple groups over function fields, self-intersections of diagonal cycles on shtuka moduli, with determinant line-bundle insertions, equal higher derivatives of adjoint L-functions.

  3. Co-periods and central symmetric cube L-values

    math.NT 2025-07 conditional novelty 7.0 of 10

    Co-period integrals of GL(2) forms with two cubic exceptional theta series are locally one-dimensional, and an explicit unramified identity matches them to the central symmetric cube L-factor ratio.

  4. Functoriality of Coulomb branches

    math.AG 2025-01 conditional novelty 7.0 of 10

    Gluable maps of reductive groups make Coulomb branches compose via Hamiltonian reduction, yielding a proof that T^*(G/U_P) for GL_n and SL_n is a Coulomb branch.

  5. Bump-Friedberg type periods beyond the cuspidal spectrum

    math.RT 2026-07 accept novelty 6.5 of 10

    Bump–Friedberg-type periods extend continuously beyond the cuspidal spectrum under regularity, and on GL_{2n+1} Eisenstein series they equal a sum of L-values indexed by dual-variety fixed points.

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