  We study the AGT 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 AGT correspondence is in a special integrable
structure which appears in the properly extended conformal theory. One of the
basic manifestations of this integrability is the special orthogonal basis
which arises in the extended theory. We propose modification of the AGT
representation for the W_N 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.
