Global quantum geometric Langlands at irrational level
We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level \(c\in\mathbb C\setminus\mathbb Q\), including non-real levels. For every smooth projective connected complex curve X, it identifies the full twisted D-module categories on \(\mathop{\mathrm{Bun}}\nolimits _G(X)\) and \(\mathop{\mathrm{Bun}}\nolimits _{G^\vee}(X)\) at the dual shifted levels c and \(-1/(rc)\), where r is the lacing number. The equivalence uses the given global forms and includes all connected components.
Cite
@misc{OAI:Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026,
author = {{OpenAI}},
title = {{Global quantum geometric Langlands at irrational level}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026/quantum-langlands.pdf}{OAI:Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026}},
year = {2026}
}