Conformal blocks of WN minimal models and AGT correspondence

We study the ACT correspondence between four-dimensional supersymmetric gauge field theory and two-dimensional conformal field theories in the context of W-N, minimal models. The origin of the ACT correspondence is in a special integrable structure winch appears in the properly extended conformal theory. One of the basic manifestations of tins integrability is the special orthogonal basis which arises in the extended theory. We propose modification of the ACT representation for the WN conformal blocks in the minimal models. The necessary modification is related to the reduction of the orthogonal basis. This leads to the explicit combinatorial representation for the conformal blocks of minimal models and employs the sum over N-tupels of Young diagrams with additional restrictions.