  Recently proposed relation between conformal field theories in two dimensions
and supersymmetric gauge theories in four dimensions predicts the existence of
the distinguished basis in the space of local fields in CFT. This basis has a
number of remarkable properties, one of them is the complete factorization of
the coefficients of the operator product expansion. We consider a particular
case of the U(r) gauge theory on C^2/Z_p which corresponds to a certain coset
conformal field theory and describe the properties of this basis. We argue that
in the case p=2, r=2 there exist different bases. We give an explicit
construction of one of them. For another basis we propose the formula for
matrix elements.
