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Transactions of the American Mathematical Society

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

   
 
 

 

Zhu reduction for Jacobi $ n$-point functions and applications


Authors: Kathrin Bringmann, Matthew Krauel and Michael Tuite
Journal: Trans. Amer. Math. Soc. 373 (2020), 3261-3293
MSC (2010): Primary 11F50, 17B69
DOI: https://doi.org/10.1090/tran/8013
Published electronically: February 11, 2020
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Abstract: We establish precise Zhu reduction formulas for Jacobi $ n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms.


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Additional Information

Kathrin Bringmann
Affiliation: Institute of Mathematics, University of Cologne, Albertus-Magnus-Platz, 50923 Köln, Germany
Email: kbringma@math.uni-koeln.de

Matthew Krauel
Affiliation: Department of Mathematics and Statistics, California State University, Sacramento, California 95819
Email: krauel@csus.edu

Michael Tuite
Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland H91 TK33
Email: michael.tuite@nuigalway.ie

DOI: https://doi.org/10.1090/tran/8013
Received by editor(s): October 11, 2018
Received by editor(s) in revised form: August 10, 2019
Published electronically: February 11, 2020
Additional Notes: 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 received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant agreement n. 335220 - AQSER
Research of the second author for this project was supported by the European Research Council (ERC) Grant agreement n. 335220 - AQSER, and also by a research visit to the Max Plank Institute for Mathematics in Bonn
Article copyright: © Copyright 2020 by the authors