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It is shown explicitly that the correlation functions of conformal field
theories (CFT) with the logarithmic operators are invariant under the
differential realization of Borel subalgebra of ${\cal W}_{\infty}$-algebra.
This algebra is constructed by tensor-operator algebra of differential
representation of ordinary $\text{sl}(2,\Bbb{C})$. This method allows us to
write
differential equations which can be used to find general expression for three-
and four-point correlation functions possessing logarithmic operators. The
operator product expansion (OPE) coefficients of general logarithmic CFT are
given up to third level.
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