Abstract
String functions are important building blocks of characters of integrable highest modules over affine Kac–Moody algebras. Kac and Peterson computed string functions for affine Lie algebras of type \(A_{1}^{(1)}\) in terms of Dedekind eta functions. We obtain new symmetries for string functions by exploiting their natural setting of Hecke-type double-sums, where special double-sums are expressed in terms of Appell–Lerch functions and theta functions, where we point out that Appell–Lerch functions are the building blocks of Ramanujan’s classical mock theta functions. We then demonstrate the utility of the new symmetries by giving new proofs of classical string function identities.
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Acknowledgements
This research was supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS, Agreement No. 20-7-1-25-1. We would also like to thank O. Warnaar and E. Feigin for helpful comments and suggestions. The authors state that there are no conflicts of interest.
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Mortenson, E.T., Postnova, O. & Solovyev, D. On string functions and double-sum formulas. Res Math Sci 10, 15 (2023). https://doi.org/10.1007/s40687-023-00379-x
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DOI: https://doi.org/10.1007/s40687-023-00379-x