Alday-Gaiotto-Tachikawa (AGT) conjecture and WZW model

In 2009 Alday, Gaiotto and Tachikawa (AGT) conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of $N=2$ super-conformal field theory. I would like to know if anything similar shows up for WZW conformal blocks. A much more elementary (but related ) question is the following: Is there any elliptic recursion for 4-point conformal blocks in WZW theory, like in Liouville theory (see e.g. these papers ). From a mathematician view-point, this relation between 4-point spheric and 1-point toric conformal blocks is not so surprising. Indeed, the moduli space $\mathcal M_{1,1}$ of elliptic curves and the unordered moduli space $\mathcal M_{0,[4]}$ of 4-punctured rational curves are the same. I would be anyway very interested in learning about recent advances in the WZW side of the story (if it exists).