Year: 2025
Type: preprint
Abstract: 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 $\mathrm{PSL}(2,\mathbb{C})$, 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.
Source: arXiv (Cornell University)
Authors: Ambrosino, Federico, Teschner, Jörg
Institutions: Deutsches Elektronen-Synchrotron DESY, Universität Hamburg
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4415317798
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