Kac-Wakimoto characters and non-holomorphic Jacobi forms
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- by Kathrin Bringmann and René Olivetto PDF
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Abstract:
In this paper, we investigate the automorphic properties of certain characters introduced by Kac and Wakimoto pertaining to $s\ell (m,n)^{\wedge }$ 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.References
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Additional Information
- Kathrin Bringmann
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- MR Author ID: 774752
- Email: kbringma@math.uni-koeln.de
- René Olivetto
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- Email: rolivett@math.uni-koeln.de
- Received by editor(s): September 2, 2014
- Received by editor(s) in revised form: March 5, 2015
- Published electronically: April 15, 2016
- Additional Notes: The research of the first author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation, and the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant agreement No. 335220 - AQSER
The research of the second author was supported by Graduiertenkolleg “Global Structures in Geometry and Analysis” - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 1163-1184
- MSC (2010): Primary 11F03, 11F22, 11F37, 11F50
- DOI: https://doi.org/10.1090/tran/6709
- MathSciNet review: 3572269