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It was recently conjectured that the AGT correspondence between the$U(r)$-instanton counting on $\mathbb R^4/\mathbb Z_p$ and the two-dimensionalfield theories with the conformal symmetry algebra $\mathcal A(r,p)$ can beconsidered as a root of unity limit of its K-theoretic analogue. From thispoint of view, the algebra $\mathcal A(r,p)$ and a special basis in itsrepresentation are limits of the Ding-Iohara algebra and the Macdonaldpolynomials respectively. In this paper we confirm this conjecture for thespecial case $r=1$. We uncover the implicit $\mathcal A(1,p)$ symmetry in thislimit. We also found that the vertex operators in the special basis havefactorized AFLT form.

AGT correspondence, Ding-Iohara algebra at roots of unity and Lepowsky-Wilson construction