  Operator product expansion (OPE) of two operators in two-dimensional
conformal field theory includes a sum over Virasoro descendants of other
operator with universal coefficients, dictated exclusively by properties of the
Virasoro algebra and independent of choice of the particular conformal model.
In the free field model, these coefficients arise only with a special
"conservation" relation imposed on the three dimensions of the operators
involved in OPE. We demonstrate that the coefficients for the three
unconstrained dimensions arise in the free field formalism when additional
Dotsenko-Fateev integrals are inserted between the positions of the two
original operators in the product. If such coefficients are combined to form an
$n$-point conformal block on Riemann sphere, one reproduces the earlier
conjectured $\beta$-ensemble representation of conformal blocks, thus proving
this (matrix model) version of the celebrated AGT relation. The statement can
also be regarded as a relation between the $3j$-symbols of the Virasoro algebra
and the slightly generalized Selberg integrals $I_Y$, associated with arbitrary
Young diagrams. The conformal blocks are multilinear combinations of such
integrals and the remaining part of the original AGT conjecture relates them to
the Nekrasov functions which have exactly the same structure.
