Combinatorial expansions of conformal blocks

A representation of Nekrasov partition functions in terms of a nontrivial two-dimensional conformal field theory was recently suggested. For a nonzero value of the deformation parameter $\epsilon=\epsilon_1+\epsilon_2$, the instanton partition function is identified with a conformal block of the Liouville theory with the central charge $c=1+6\epsilon^2/\epsilon_1\epsilon_2$. The converse of this observation means that the universal part of conformal blocks, which is the same for all two-dimensional conformal theories with nondegenerate Virasoro representations, has a nontrivial decomposition into a sum over Young diagrams that differs from the natural decomposition studied in conformal field theory. We provide some details about this new nontrivial correspondence in the simplest case of the four-point correlation functions.