Vertex algebra constructions for (analytic) geometric Langlands in genus zero

A bstract We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program. In particular, we build “Multiplication Kernels” K 3 (x, x′, x′′) which intertwine the action of sl₂ s l 2 Gaudin Hamiltonians on three sets of variables.