On characters of L_\fraksl_n(-Λ₀)-modules

2018/03/21 by Kathrin Bringmann, Bringmann, Kathrin, Karl Mahlburg +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1803.08029

openalex publication_date 2018/03/21 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We use recent results of Rolen, Zwegers, and the first author to study characters of irreducible (highest weight) modules for the vertex operator algebra L_\fraksl_ℓ(-Λ₀). We establish asymptotic behaviors of characters for the (ordinary) irreducible L_\fraksl_ℓ(-Λ₀)-modules. As a consequence we prove that their quantum dimensions are one, as predicted by representation theory. We also establish a full asymptotic expansion of irreducible characters for \fraksl₃. Finally, we determine a decomposition formula for the full characters in terms of unary theta and false theta functions which allows us to study their modular properties.

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