Proof of 5D A n AGT conjecture at β = 1

Abstract In this paper, we give a proof of 5D A n AGT conjecture at β = 1, 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 A n Selberg integral, which generalizes the A n Selberg integral and the q-deformed A 1 Selberg integral in the literature. A q-deformed A n Selberg average formula with n + 1 Schur polynomials is proposed and proved to complete the proof.