W-algebras, higher rank false theta functions, and quantum dimensions

Abstract

Motivated by appearances of Rogers’ false theta functions in the representation theory of the singlet vertex operator algebra, for each finite-dimensional simple Lie algebra of ADE type, we introduce higher rank false theta functions as characters of atypical modules of certain W-algebras and compute asymptotics of irreducible characters which allows us to determine quantum dimensions of the corresponding modules. In the \({{\text {s}}\ell }_2\)-case, we recover many results from Bringmann and Milas (IMRN 21:11351–11387, 2015).