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A recent claim that the S-duality between 4d SUSY gauge theories, which isAGT related to the modular transformations of 2d conformal blocks, is no morethan an ordinary Fourier transform at the perturbative level, is further traceddown to the commutation relation [P,Q]=-i\hbar between the check-operatormonodromies of the exponential resolvent operator in the underlyingDotsenko-Fateev matrix models and beta-ensembles. To this end, we treat theconformal blocks as eigenfunctions of the monodromy check operators, what isespecially simple in the case of one-point toric block. The kernel of themodular transformation is then defined as the intertwiner of the twomonodromies, and can be obtained straightforwardly, even when the eigenfunctioninterpretation of the blocks themselves is technically tedious. In this way, weprovide an elementary derivation of the old expression for the modular kernelfor the one-point toric conformal block.

S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality