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An intriguing coincidence between the partition function of super Yang-Millstheory and correlation functions of 2d Toda system has been heavily studiedrecently. While the partition function of gauge theory was explored byNekrasov, the correlation functions of Toda equation have not been completelyunderstood. In this paper, we study the latter in the form of Dotsenko-Fateevintegral and reduce it in the form of Selberg integral of several Jackpolynomials. We conjecture a formula for such Selberg average which satisfiessome consistency conditions and show that it reproduces the SU(N) version ofAGT conjecture.

Selberg Integral and SU(N) AGT Conjecture