A general framework for the analytic Langlands correspondence
Abstract
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.
Keywords
Cite
@article{arxiv.2311.03743,
title = {A general framework for the analytic Langlands correspondence},
author = {Pavel Etingof and Edward Frenkel and David Kazhdan},
journal= {arXiv preprint arXiv:2311.03743},
year = {2024}
}
Comments
85 pages; v2: new material added in Section 3, including an analogue of the Langlands functoriality principle in the analytic Langlands correspondence