TY - JOUR

T1 - On string functions and double-sum formulas

AU - Mortenson, Eric T.

AU - Постнова, Ольга Викторовна

AU - Соловьёв, Дмитрий Павлович

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

U2 - 10.1007/s40687-023-00379-x

DO - 10.1007/s40687-023-00379-x

M3 - Article

VL - 10

JO - Research in the Mathematical Sciences

JF - Research in the Mathematical Sciences

SN - 2522-0144

M1 - 15

ER -