%0 Journal Article
%T Conjugate Bailey pairs
%A Anne Schilling
%A S. Ole Warnaar
%J Mathematics
%D 1999
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9906092v1