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

Lev Spodyneiko

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arXiv · 1409.3465

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

Lev Spodyneiko

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Abstract

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

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Lev Spodyneiko. 2014-09-10. AGT correspondence, Ding-Iohara algebra at roots of unity and Lepowsky-Wilson construction. https://arxiv.org/abs/1409.3465

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