Related established frameworks

Kapustin–Witten formulate a gauge-theoretic geometric Langlands programme using a topologically twisted four-dimensional $\mathcal{N}=4$ theory compactified on a curve KapustinWitten. Gaitsgory's quantum Langlands notes and Whittaker comparison work concern independently stated categorical and sheaf-theoretic interfaces GaitsgoryQGL,GaitsgoryWhit. Arakawa–Frenkel prove named $W$-algebra representation dualities ArakawaFrenkel.

Abelian Fourier transforms for differential-operator algebras have their own geometric statements PolishchukRothstein. Our finite Fourier construction below is proved directly; it is not substituted for those transforms.

The AdS/CFT proposal involves further choices and limits, including the large-$N$ setting described by Maldacena Maldacena. The Kapustin–Witten motivation does not identify the present finite task with that dictionary.