Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Kac-Wakimoto characters and non-holomorphic Jacobi forms


Authors: Kathrin Bringmann and René Olivetto
Journal: Trans. Amer. Math. Soc. 369 (2017), 1163-1184
MSC (2010): Primary 11F03, 11F22, 11F37, 11F50
DOI: https://doi.org/10.1090/tran/6709
Published electronically: April 15, 2016
MathSciNet review: 3572269
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11F03, 11F22, 11F37, 11F50

Retrieve articles in all journals with MSC (2010): 11F03, 11F22, 11F37, 11F50


Additional Information

Kathrin Bringmann
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
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

DOI: https://doi.org/10.1090/tran/6709
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”
Article copyright: © Copyright 2016 American Mathematical Society