A gauge theory duality between the low energy effective theory of 5D N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1 will be expolored in this talk. The duality is found by using both the Seiberg-Witten formalism and the topological vertex formalism. The duality map between the gauge theory parameters will be given. I will also discuss some implications of this duality in the context of the AGT conjecture.
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