Selecta Mathematica

, Volume 23, Issue 2, pp 1249–1278 | Cite as

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

  • Kathrin Bringmann
  • Antun MilasEmail author


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).


Characters False theta functions Jacobi forms Modular forms Vertex algebras 

Mathematics Subject Classification

17B69 14K25 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of CologneCologneGermany
  2. 2.Department of Mathematics and StatisticsSUNY-AlbanyAlbanyUSA

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