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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The mock modular data of a family of superalgebras
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by Claudia Alfes and Thomas Creutzig PDF
Proc. Amer. Math. Soc. 142 (2014), 2265-2280 Request permission

Abstract:

The modular properties of characters of representations of a family of W-superalgebras extending $\widehat {\mathfrak {gl}}(1|1)$ are considered. Modules fall into two classes, the generic type and the non-generic one. Characters of non-generic modules are expressed in terms of higher-level Appell-Lerch sums. We compute the modular transformations of characters and interpret the Mordell integral as an integral over characters of generic representations. The $\mathbb {C}$-span of a finite number of non-generic characters together with an uncountable set of characters of the generic type combine into a representation of $\mathrm {SL}(2;Z)$. The modular transformations are then used to define a product on the space of characters. The fusion rules of the extended algebras are partially inherited from the known fusion rules for modules of $\widehat {\mathfrak {gl}}(1|1)$. Moreover, the product obtained from the modular transformations coincides with the product of the Grothendieck ring of characters if and only if the fusion multiplicities are at most one.
References
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Additional Information
  • Claudia Alfes
  • Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
  • Email: alfes@mathematik.tu-darmstadt.de
  • Thomas Creutzig
  • Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
  • Address at time of publication: Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
  • MR Author ID: 832147
  • ORCID: 0000-0002-7004-6472
  • Email: creutzig@ualberta.ca
  • Received by editor(s): July 19, 2012
  • Published electronically: April 3, 2014
  • Communicated by: Ken Ono
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2265-2280
  • MSC (2010): Primary 11F22, 11F37, 81T40
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11959-9
  • MathSciNet review: 3195752