Analytic Langlands correspondence from SoV
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918297572737024 |
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| author | Ambrosino, Federico Teschner, Jörg |
| author_facet | Ambrosino, Federico Teschner, Jörg |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Langlands correspondence from SoV Ambrosino, Federico Teschner, Jörg Functional Analysis High Energy Physics - Theory Algebraic Geometry Representation Theory 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. |
| title | Analytic Langlands correspondence from SoV |
| topic | Functional Analysis High Energy Physics - Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2510.06991 |