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We propose and demonstrate a limiting procedure in which, starting from theq-lifted version (or K-theoretic five dimensional version) of the (W)AGTconjecture to be assumed in this paper, the Virasoro/W block is generated inthe r-th root of unity limit in q in the 2d side, while the same limitautomatically generates the projection of the five dimensional instantonpartition function onto that on the ALE space R^4/Z_r. This circumventscase-by-case conjectures to be made in a wealth of examples found so far. Inthe 2d side, we successfully generate the super-Virasoro algebra and the properscreening charge in the q -> -1, t -> -1 limit, from the defining relation ofthe q-Virasoro algebra and the q-deformed Heisenberg algebra. The centralcharge obtained coincides with that of the minimal series carrying odd integersof the N=1 superconformal algebra. In the r-th root of unity limit in q in the2d side, we give some evidence of the appearance of the parafermion-likecurrents. Exploiting the q-analysis literatures, q-deformed su(n) block isreadily generated both at generic q, t and the r-th root of unity limit. In the4d side, we derive the proper normalization function for general (n, r) thataccomplishes the automatic projection through the limit.

2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space