1999/06/14 by Anne Schilling, Schilling, Anne, S. Ole Warnaar +1 · 1 citation
Mathematics · #05A19 #17B67 #33D90 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A30 #Quantum Algebra (math.QA) #Secondary 82B23 #math.CO #math.QA #msc:05A19 #msc:05A30 #msc:17B67 #msc:33D90 #msc:82B23
paper · pdf · doi:10.48550/arxiv.math/9906092
29 pages, AMS-LaTeX
arxiv created 1999/06/14 · openalex publication_date 1999/06/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 A1(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 A1(1) branching functions. In addition, q-series identities are obtained whose Lie algebraic and/or combinatorial interpretation is still lacking.