The geometric correspondence between the Bethe ansatz solution of the Gaudin model and correlation functions of WZNW models, which was proposed by Feigin, Frenkel and Reshetikhin, is an ideal framework for studying the conformal properties of W structures, which are obtained by Hamiltonian reduction. There, it is always possible to find a projective parameterization when conformal covariance is imposed via zero curvature conditions.
It would be very interesting to discuss this point in the context of Langlands correspondence in order to get a better understanding. A prominent example to start with are the two SL(2) embeddings of SL(3). It also seems to be very promising to find a supersymmetric extension of Langlands duality, which would establish a deep relationship between the OSp(1,2) Gaudin model and the corresponding superconformal structures for W algebras. From the view-point of statistical physics another interesting task is to try to generalize the proof of the completeness of the Bethe ansatz given by Frenkel to other integrable quantum spin chains.