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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 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 fractionallevel 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. 0. Notation Throughout the paper the following notation is used. N are the positive integers, Z+ the nonnegative integers, Np = {1, . . . , p}, Zp = {0, . . . , p − 1}. For n ∈ Z, ( n 2 ) = n(n− 1)/2. 1. The Bailey lemma In an attempt to clarify Rogers’ second proof [60] of the Rogers–Ramanujan identities, Bailey [19] was led to the following simple but important observation. Lemma 1.1. If α = {αL}L≥0, . . . , δ = {δL}L≥0 are sequences that satisfy

Conjugate Bailey pairs: from configuration sums and fractional-level string functions to Bailey’s lemma