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Conjugate Bailey pairs

Anne Schilling·S. Ole Warnaar
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Abstract

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.

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Anne Schilling, S. Ole Warnaar. 1999-06-14. Conjugate Bailey pairs. https://arxiv.org/abs/math/9906092

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