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).
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Bringmann, K., Milas, A. W-algebras, higher rank false theta functions, and quantum dimensions. Sel. Math. New Ser. 23, 1249–1278 (2017). https://doi.org/10.1007/s00029-016-0289-z
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DOI: https://doi.org/10.1007/s00029-016-0289-z