Generalized Rogers Ramanujan Identities from AGT Correspondence

Abstract

AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset $\mathcal{A}(r,p)=U(1)\times sl(p{)}_r\times \frac{sl(r{)}_p\times sl(r{)}_n}{sl(r{)}_{n+p}}$, where $n$ is a parameter. Our purpose here is to describe Generalized Rogers Ramanujan (GRR) identities for these cosets, which expresses the characters as certain $q$ series. We propose that such identities exist for the coset $\mathcal{A}(r,p)$ for all positive integers $n$ and all $r$ and $p$. We treat here the case of $n=1$ and $r=2$, finding GRR identities for all the characters.

11 pages

Cited by in corpus (7)

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• The $\mathbf{SO}(2\mathbf{r}{)}_2$ string functions as $\mathbf{q}$-diagrams
• Generalized Rogers Ramanujan Identities for Twisted Affine Algebras