Conjugate Bailey pairs

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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 A₁⁽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 A₁⁽¹⁾ branching functions. In addition, q-series identities are obtained whose Lie algebraic and/or combinatorial interpretation is still lacking.