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Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity

Journal of High Energy Physics. 2013. No. 3. P. 1-36.
Belavin A., Bershtein M., Tarnopolsky G.

A bstract We continue our study of the AGT correspondence between instanton counting on
${{{{{\ mathbb {C}}^ 2}}}\ left/{{{{\ mathbb {Z}} _p}}}\ right.}$ and Conformal field theories with
the symmetry algebra $\ mathcal {A}\ left ({r, p}\ right)$. In the cases r= 1, p= 2 and r= 2, p= 2
this algebra specialized to: $\ mathcal {A}\ left ({1, 2}\ right)=\ mathcal {H}\ oplus\ widehat {\ mathfrak {sl}}{(2) _1}$ and $\ mathcal {A}\ left ({2, 2}\ right)=\ mathcal {H}\ oplus\ widehat {\ mathfrak {sl}}{(2) _2}\ oplus\ mathrm {NSR}$.