  In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa
proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric
gauge theories and two-dimensional conformal field theories. As part of their
conjecture they gave an explicit combinatorial formula for the expansion of the
conformal blocks inspired from the exact form of instanton part of the Nekrasov
partition function. In this paper we study the origin of such an expansion from
a CFT point of view. We consider the algebra $\mathcal{A}=\text{\sf
Vir}\otimes\mathcal{H}$ which is the tensor product of mutually commuting
Virasoro and Heisenberg algebras and discover the special orthogonal basis of
states in the highest weight representations of $\mathcal{A}$. The matrix
elements of primary fields in this basis have a very simple factorized form and
coincide with the function called $Z_{\text{\sf{bif}}}$ appearing in the
instanton counting literature. Having such a simple basis, the problem of
computation of the conformal blocks simplifies drastically and can be shown to
lead to the expansion proposed in \cite{Alday:2009aq}. We found that this basis
diagonalizes an infinite system of commuting Integrals of Motion related to
Benjamin-Ono integrable hierarchy.
