Simplicity of vacuum modules over affine Lie superalgebras

Crystal Hoyt, Shifra Reif

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We prove an explicit condition on the level k for the irreducibility of a vacuum module Vk over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level k is a non-negative integer.

Original languageEnglish
Pages (from-to)2861-2874
Number of pages14
JournalJournal of Algebra
Issue number10
StatePublished - 15 May 2009
Externally publishedYes


  • Affine Lie superalgebra
  • Vacuum module
  • W-algebra


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