Alfes C, Creutzig T (2014)
Publication Type: Journal article
Publication year: 2014
Book Volume: 142
Pages Range: 2265-2280
Journal Issue: 7
DOI: 10.1090/S0002-9939-2014-11959-9
The modular properties of characters of representations of a family of W-superalgebras extending 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 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 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 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.
APA:
Alfes, C., & Creutzig, T. (2014). The mock modular data of a family of superalgebras. Proceedings of the American Mathematical Society, 142(7), 2265-2280. https://doi.org/10.1090/S0002-9939-2014-11959-9
MLA:
Alfes, Claudia, and Thomas Creutzig. "The mock modular data of a family of superalgebras." Proceedings of the American Mathematical Society 142.7 (2014): 2265-2280.
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