From Configuration Sums and Fractional-level String Functions to Bailey’s Lemma

نویسنده

  • ANNE SCHILLING
چکیده

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 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.

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تاریخ انتشار 1999