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arXiv · 2107.06225

On string functions and double-sum formulas

Eric T. Mortenson·Olga Postnova·Dmitry Solovyev
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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 produce new relations between string functions by writing them as double-sums and then using certain symmetry relations. We evaluate the series using special double-sum formulas that express Hecke-type double-sums 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.

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Eric T. Mortenson, Olga Postnova, Dmitry Solovyev. 2021-07-13. On string functions and double-sum formulas. https://doi.org/10.1007/s40687-023-00379-x

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