1211.2788 (A. A. Belavin et al.)

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

A. A. Belavin, M. A. Bershtein, G. M. Tarnopolsky

We continue our study of AGT correspondence between instanton counting on C^2/\Z_p 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+sl(2)_1 and A(2,2)=H+sl(2)_2+NSR. As the main tool we use new construction of the algebra A(r,2) as the limit of the toroidal gl(1) algebra for q,t tends 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 tends 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 N=1 Super Virasoro algebra can be realized in terms of Macdonald polynomials for rectangular Young diagram and parameters q,t tends to -1.

View original: http://arxiv.org/abs/1211.2788