Almost harmonic Maass forms and Kac-Wakimoto characters
Number Theory
2013-03-05 v2
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.
Keywords
Cite
@article{arxiv.1112.4726,
title = {Almost harmonic Maass forms and Kac-Wakimoto characters},
author = {Kathrin Bringmann and Amanda Folsom},
journal= {arXiv preprint arXiv:1112.4726},
year = {2013}
}
Comments
To appear in J. Reine Angew. Math. (Crelle's Journal). This final version updates prior arXiv submission 1112.4726