Almost harmonic Maass forms and Kac-Wakimoto characters

Details Almost harmonic Maass forms and Kac-Wakimoto characters Almost harmonic Maass forms and Kac-Wakimoto characters

2011-12-20

arxiv.org/abs/1112.4726v1

Mathematics

Number Theory

Scientific paper

In this paper, we investigate 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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