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Namely we check the correspondence between the SU(2) Nekrasov partition function on $\\mathbb{R}^{4}/\\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. 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