2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78662In 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.29 pages, AMS-LaTeXQuantum AlgebraCombinatoricsPrimary 05A30, 05A19; Secondary 82B23, 17B67, 33D90text