Almost harmonic Maass forms and Kac-Wakimoto characters

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.

To appear in J. Reine Angew. Math. (Crelle's Journal). This final version updates prior arXiv submission 1112.4726

References in corpus (4)

• Mock Theta Functions
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Asymptotics for rank and crank moments
• Topological Strings and (Almost) Modular Forms

Cited by in corpus (4)

• Representations of affine superalgebras and mock theta functions III
• Mordell integrals and Giveon-Kutasov duality
• The Mock Modular Data of a Family of Superalgebras
• Negative index Jacobi forms and quantum modular forms