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.
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