Quantum Betti geometric Langlands functor

Abstract

We construct the quantum geometric Langlands functor in the Betti setting via Whittaker coefficients. We show that the functor is compatible with the 2-Fourier-Mukai equivalence between sheaves of categories over 2-stacks ${\mathrm{Ge}}_{Z_G}$ and ${\mathrm{Ge}}_{\ddot{I}{€}_1(\check{G})}$, which classify gerbes on $X$ with respect to the center $Z_G$ of $G$ and algebraic fundamental group $\ddot{I}{€}_1(\check{G})$ of $\check{G}$.

30 pages; comments welcome