Conjugate Bailey pairs

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.

29 pages, AMS-LaTeX

References in corpus (10)

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Cited by in corpus (8)

• Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)
• On string functions and double-sum formulas
• Permutation Orbifold of N=2 Supersymmetric Minimal Models
• On Hecke-type double-sums and general string functions for the affine Lie algebra $A_1^{(1)}$
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• Staggered and affine Kac modules over $A_1^{(1)}$
• Path representation of su(2)_k states I: Operators and particles for k=1,2
• The Bailey lemma and Kostka polynomials