We continue our study of the AGT correspondence between instanton counting on C/Zp and Conformal field theories with the symmetry algebra A(r,p). In the cases r = 1, p = 2 and r = 2, p = 2 this algebra specialized to: A(1,2) = H sI(2)1 and A(2,2) = H sI(2)2 NSR. As the main tool we use a new construction of the algebra A(r, 2) as the limit of the toroidal aI(1) algebra for q, t tend to -1. We claim that the basis of the representation of the algebra A(r/2) (or equivalently, of the space of the local fields of the corresponding CFT) can be expressed through Macdonald polynomials with the parameters q, t go to -1. The vertex operator which naturally arises in this construction has factorized matrix elements in this basis. We also argue that the singular vectors of the N=1 Super Virasoro algebra can be realized in terms of Macdonald polynomials for a rectangular Young diagram and parameters q, t tend to -1. © 2013 SISSA, Trieste, Italy.
CITATION STYLE
Belavin, A. A., Bershtein, M. A., & Tarnopolsky, G. M. (2013). Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity. Journal of High Energy Physics, 2013(3). https://doi.org/10.1007/JHEP03(2013)019
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