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arXiv · 1803.08029

On characters of $L_{\frak{sl}_n}(-\Lambda_0)$-modules

Kathrin Bringmann·Karl Mahlburg·Antun Milas
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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 $L_{\frak{sl}_\ell}(-\Lambda_0)$. We establish asymptotic behaviors of characters for the (ordinary) irreducible $L_{\frak{sl}_\ell}(-\Lambda_0)$-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 $\frak{sl}_3$. 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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Kathrin Bringmann, Karl Mahlburg, Antun Milas. 2018-03-21. On characters of $L_{\frak{sl}_n}(-\Lambda_0)$-modules. https://arxiv.org/abs/1803.08029

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