On string functions and double-sum formulas

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.

24 pages

References in corpus (1)

• Mock Theta Functions

Cited by in corpus (3)

• On Hecke-type double-sums and general string functions for the affine Lie algebra $A_1^{(1)}$
• Two $2/5$-level mock theta conjecture-like identities
• Unimodal sequences and mixed false theta functions