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arXiv · 1112.4726

Almost harmonic Maass forms and Kac-Wakimoto characters

Kathrin Bringmann·Amanda Folsom
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Abstract

We resolve a question of Kac, and explain the automorphic properties of characters due to Kac-Wakimoto pertaining to sl(m|n)^ highest weight modules, for n \geq 1. We prove that the Kac-Wakimoto characters are essentially holomorphic parts of certain generalizations of harmonic weak Maass forms which we call "almost harmonic Maass forms". Using a new approach, this generalizes prior work of the first author and Ono, and the authors, both of which treat only the case n = 1. We also provide an explicit asymptotic expansion for the characters.

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Kathrin Bringmann, Amanda Folsom. 2013-03-03. Almost harmonic Maass forms and Kac-Wakimoto characters. https://arxiv.org/abs/1112.4726

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