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

Kathrin Bringmann ^[1] ; Antun Milas ^[2]
1. [1] University of Cologne
  
  University of Cologne
  
  Kreisfreie Stadt Köln, Alemania
2. [2] Department of Mathematics and Statistics
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1249-1278
Idioma: inglés
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Resumen
- 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 s 2-case, we recover many results from Bringmann and Milas (IMRN 21:11351–11387, 2015).