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In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset ${\\cal A}(r,p)=U(1)\\times sl(p)_r\\times {sl(r)_p\\times sl(r)_n\\over sl(r)_{n+p}}$, 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 ${\\cal A}(r,p)$ for all positive integers $n$ and all $r$ and $p$. 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