  In this paper it is shown that the one-dimensional configuration sums of the
solvable lattice models of Andrews, Baxter and Forrester and the string
functions associated with admissible representations of the affine Lie algebra
A$_1^{(1)}$ as introduced by Kac and Wakimoto can be exploited to yield a very
general class of conjugate Bailey pairs. Using the recently established
fermionic or constant-sign expressions for the one-dimensional configuration
sums, our result is employed to derive fermionic expressions for
fractional-level string functions, parafermion characters and A$_1^{(1)}$
branching functions. In addition, $q$-series identities are obtained whose Lie
algebraic and/or combinatorial interpretation is still lacking.
