A general framework for the analytic Langlands correspondence
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913233063903232 |
|---|---|
| author | Etingof, Pavel Frenkel, Edward Kazhdan, David |
| author_facet | Etingof, Pavel Frenkel, Edward Kazhdan, David |
| contents | We discuss a general framework for the analytic Langlands correspondence over an arbitrary local field F introduced and studied in our works arXiv:1908.09677, arXiv:2103.01509 and arXiv:2106.05243, in particular including non-split and twisted settings. Then we specialize to the archimedean cases (F=C and F=R) and give a (mostly conjectural) description of the spectrum of the Hecke operators in various cases in terms of opers satisfying suitable reality conditions, as predicted in part in arXiv:2103.01509, arXiv:2106.05243 and arXiv:2107.01732. We also describe an analogue of the Langlands functoriality principle in the analytic Langlands correspondence over C and show that it is compatible with the results and conjectures of arXiv:2103.01509. Finally, we apply the tools of the analytic Langlands correspondence over archimedean fields in genus zero to the Gaudin model and its generalizations, as well as their q-deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03743 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A general framework for the analytic Langlands correspondence Etingof, Pavel Frenkel, Edward Kazhdan, David Algebraic Geometry High Energy Physics - Theory Number Theory Representation Theory Exactly Solvable and Integrable Systems We discuss a general framework for the analytic Langlands correspondence over an arbitrary local field F introduced and studied in our works arXiv:1908.09677, arXiv:2103.01509 and arXiv:2106.05243, in particular including non-split and twisted settings. Then we specialize to the archimedean cases (F=C and F=R) and give a (mostly conjectural) description of the spectrum of the Hecke operators in various cases in terms of opers satisfying suitable reality conditions, as predicted in part in arXiv:2103.01509, arXiv:2106.05243 and arXiv:2107.01732. We also describe an analogue of the Langlands functoriality principle in the analytic Langlands correspondence over C and show that it is compatible with the results and conjectures of arXiv:2103.01509. Finally, we apply the tools of the analytic Langlands correspondence over archimedean fields in genus zero to the Gaudin model and its generalizations, as well as their q-deformations. |
| title | A general framework for the analytic Langlands correspondence |
| topic | Algebraic Geometry High Energy Physics - Theory Number Theory Representation Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2311.03743 |