2025/10/08 by Federico Ambrosino, Ambrosino, Federico, Jörg Teschner +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2510.06991
openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
The analytic Langlands correspondence proposed by Etingof, Frenkel and Kazhdan describes the solution to the spectral problems naturally arising in the quantisation of the Hitchin integrable systems in terms of real opers, certain second order differential operators on a Riemann surface having real monodromy. We prove this correspondence in the cases associated to the group PSL(2,ℂ), and Riemann surfaces of genus zero with a number of punctures larger than three. A crucial ingredient is a unitary integral transformation mapping products of solutions to the ordinary differential equation associated to a real oper to eigenfunctions of the quantised Hitchin Hamiltonians. This allows us to construct joint eigenfunctions of Hecke operators and Hitchin Hamiltonians from real opers.