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
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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.
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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”
Article copyright:
© Copyright 2016
American Mathematical Society