Bailey flows and Bose-Fermi identities for the conformal coset models $(A^{(1)}_1)_Ntimes (A^{(1)}_1)_{N}/(A^{(1)}_1)_{N+N}$

We use the recently established higher-level Bailey lemma and Bose-Fermi polynomial identities for the minimal models $M(p,p)$ to demonstrate the existence of a Bailey flow from $M(p,p)$ to the coset models $(A^{(1)}_1)_Ntimes (A^{(1)}_1)_{N}/(A^{(1)}_1)_{N+N}$ where $N$ is a positive integer and $N$ is fractional, and to obtain Bose-Fermi identities for these models. The fermionic side of these identities is expressed in terms of the fractional-level Cartan matrix introduced in the study of $M(p,p)$. Relations between Bailey and renormalization group flow are discussed.