Abstract
This paper deals with the five-dimensional pure SU(2) Alday-Gaiotto-Tachikawa (AGT) conjecture proposed by Awata and Yamada [J. High. Energy Phys. 1001, 125 (2010)]. We give a conjecture on a recursive formula for the inner product of the deformed Gaiotto state. We also show that the K-theoretic pure SU(2) Nekrasov partition function satisfies the same recursion relation. Therefore the five-dimensional AGT conjecture is reduced to our conjectural recursive formula.
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