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In this paper, we give a proof of 5D AGT conjecture at , where the gauge theory side is one dimension higher than the original 4D case, and corresponds to the q-deformation of the 2D conformal field theory side. We define a q-deformed Selberg integral, which generalizes the Selberg integral and the q-deformed Selberg integral in the literature. A q-deformed Selberg average formula with Schur polynomials is proposed and proved to complete the proof.

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