On Characters of Irreducible Highest Weight Modules of Negative Integer Level over Affine Lie Algebras

  • Victor G. KacEmail author
  • Minoru Wakimoto
Part of the Progress in Mathematics book series (PM, volume 326)


We prove a character formula for irreducible highest weight modules over a simple affine vertex algebra of level k, attached to a simple Lie algebra g, which are locally g-finite, in the cases when g is of type An andCn (n≥2) and k = −1. We also conjecture a character formula for types D4, E6, E7, E8 and levels k = −1, ..., −b, where b = 2, 3, 4, 6 respectively.


Free field construction character of a highestweightmodule Deligne exceptional series theta functions 

Mathematics Subject Classification (2010):

17B67 (Primary) 17B65 17B10 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics M.I.TCambridgeUSA
  2. 2.KobeJapan

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