KAC-WAKIMOTO CHARACTERS AND NON-HOLOMORPHIC JACOBI FORMS

In this paper, we investigate the automorphic properties of certain characters introduced by Kac and Wakimoto pertaining to sl(m,n)<^> highest weight modules. Extending previous work of the first author and Ono, the first author and Folsom, and the second author, we investigate the general case, not specializing the Jacobi variables. We prove that the Kac-Wakimoto characters are essentially holomorphic parts of multivariable mixed H-harmonic Maass-Jacobi forms, which are certain non-holomorphic generalizations of classical holomorphic Jacobi forms. This also gives extra structure to the previous considered cases.