Description
The analytic Langlands correspondence can be regarded as a variant of the geometric Langlands correspondence imposing additional conditions of analytic nature.
It predicts a correspondence between opers with real holonomy and eigenfunctions of the quantised Hitchin system. We will discuss a one-parameter deformation of this correspondence called quantum analytic Langlands correspondence. This deformation has natural relations to the quantisation of moduli spaces, the separation of variables, and conformal field theory. A key role is played by the Verlinde line operators. These operators represent a quantum deformation of the grafting operation creating eigenstates of the quantum Hitchin system from a cyclic vector. This is joint work with D. Gaiotto.
